Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Jesus M. F. Castillo, Yolanda Moreno and Jesus Suarez
by Dale Alspach 10 Feb '05

10 Feb '05

This is an announcement for the paper "On Lindenstrauss-Pelczynski spaces" by Jesus M. F. Castillo, Yolanda Moreno and Jesus Suarez. Abstract: In this work we shall be concerned with some stability aspects of the classical problem of extension of $C(K)$-valued operators. We introduce the class $\mathscr{LP}$ of Banach spaces of Lindenstrauss-Pe\l czy\'{n}sky type as those such that every operator from a subspace of $c_0$ into them can be extended to $c_0$. We show that all $\mathscr{LP}$-spaces are of type $\mathcal L_\infty$ but not the converse. Moreover, $\mathcal L_\infty$-spaces will be characterized as those spaces $E$ such that $E$-valued operators from $w^*(l_1,c_0)$-closed subspaces of $l_1$ extend to $l_1$. Complemented subspaces of $C(K)$ and separably injective spaces are subclasses of $\mathscr{LP}$-spaces and we show that the former does not contain the latter. It is established that $\mathcal L_\infty$-spaces not containing $l_1$ are quotients of $\mathscr{LP}$-spaces, while $\mathcal L_\infty$-spaces not containing $c_0$, quotients of an $\mathscr{LP}$-space by a separably injective space and twisted sums of $\mathscr{LP}$-spaces are $\mathscr{LP}$-spaces. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; 46M99; 46B07 The source file(s), CastilloMorenoLP.tex: 49873 bytes, is(are) stored in gzipped form as 0502081.gz with size 15kb. The corresponding postcript file has gzipped size 72kb. Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0502081 or http://arXiv.org/abs/math.FA/0502081 or by email in unzipped form by transmitting an empty message with subject line uget 0502081 or in gzipped form by using subject line get 0502081 to: math(a)arXiv.org.

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Abstract of a paper by Valentin Ferenczi
by Dale Alspach 04 Feb '05

04 Feb '05

This is an announcement for the paper "Minimality, homogeneity and topological 0-1 laws for subspaces of a Banach space" by Valentin Ferenczi. Abstract: If a Banach space is saturated with basic sequences whose linear span embeds into the linear span of any subsequence, then it contains a minimal subspace. It follows that any Banach space is either ergodic or contains a minimal subspace. If $X$ is a Banach space with a Schauder basis, the relation $E_0$ is Borel reducible to permutative equivalence between normalized block-sequences of $X$, or $X$ is $c_0$-saturated or $l_p$-saturated for some $1 \leq p <+\infty$. For a Banach space $X$ with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of $X$ as well as for subspaces of $X$ with a successive FDD on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach space with an unconditional basis, which has a complemented subspace without an unconditional basis, are deduced. Archive classification: Functional Analysis; Combinatorics Mathematics Subject Classification: 46B03; 46B15 The source file(s), ferenczitopolaw.tex: 93769 bytes, is(are) stored in gzipped form as 0502054.gz with size 26kb. The corresponding postcript file has gzipped size 99kb. Submitted from: ferenczi(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0502054 or http://arXiv.org/abs/math.FA/0502054 or by email in unzipped form by transmitting an empty message with subject line uget 0502054 or in gzipped form by using subject line get 0502054 to: math(a)arXiv.org.

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Abstract of a paper by Harald Hanche-Olsen
by Dale Alspach 04 Feb '05

04 Feb '05

This is an announcement for the paper "On the uniform convexity of L^p" by Harald Hanche-Olsen. Abstract: We present a short, direct proof of the uniform convexity of L^p spaces for 1<p<\infty. Archive classification: Functional Analysis Mathematics Subject Classification: 46E30 The source file(s), uc2.tex: 7706 bytes, is(are) stored in gzipped form as 0502021.gz with size 3kb. The corresponding postcript file has gzipped size 26kb. Submitted from: hanche(a)math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0502021 or http://arXiv.org/abs/math.FA/0502021 or by email in unzipped form by transmitting an empty message with subject line uget 0502021 or in gzipped form by using subject line get 0502021 to: math(a)arXiv.org.

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Abstract of a paper by Sasha Sodin
by Dale Alspach 26 Jan '05

26 Jan '05

This is an announcement for the paper "Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension" by Sasha Sodin. Abstract: If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show applications to measures of geometric origin. Archive classification: Metric Geometry; Functional Analysis Remarks: 29 pages The source file(s), all3.tex: 62865 bytes, is(are) stored in gzipped form as 0501382.gz with size 19kb. The corresponding postcript file has gzipped size 96kb. Submitted from: a_sodin(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0501382 or http://arXiv.org/abs/math.MG/0501382 or by email in unzipped form by transmitting an empty message with subject line uget 0501382 or in gzipped form by using subject line get 0501382 to: math(a)arXiv.org.

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Abstract of a paper by Rafal Latal and Krzysztof Oleszkiewicz
by Dale Alspach 26 Jan '05

26 Jan '05

This is an announcement for the paper "Small ball probability estimates in terms of width" by Rafal Latal and Krzysztof Oleszkiewicz. Abstract: A certain inequality conjectured by Vershynin is studied. It is proved that for any $n$-dimensional symmetric convex body $K$ with inradius $w$ and $\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK) \leq (2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false. Archive classification: Probability; Functional Analysis Mathematics Subject Classification: 60G15, 60E15 Remarks: 10 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: rlatala(a)mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.PR/0501268 or http://arXiv.org/abs/math.PR/0501268 or by email in unzipped form by transmitting an empty message with subject line uget 0501268 or in gzipped form by using subject line get 0501268 to: math(a)arXiv.org.

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Lectureship in Analysis at Leeds
by J R Partington 26 Jan '05

26 Jan '05

There is a lectureship in Analysis (a permanent position) currently advertised at the School of Mathematics, University of Leeds, U.K. The closing date for applications is March 1st 2005. Further details are available by following the link from http://wwwnotes2.leeds.ac.uk/jobs/unijob.nsf/Academic?OpenView Details of the Functional Analysis group at Leeds can be found at http://maths.leeds.ac.uk/pure/analysis/index.html Informal enquiries can be directed to Professors M.J. Wilson (Chairman of the School), mike(a)maths.leeds.ac.uk, J.C. Wood (Head of Pure Mathematics), j.c.wood(a)leeds.ac.uk, or J.R. Partington, j.r.partington(a)leeds.ac.uk.

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Conference on Banach spaces and their Applications in Analysis
by Dale Alspach 25 Jan '05

25 Jan '05

Conference Announcement: ``Banach spaces and their applications in Analysis'', in honor of Nigel Kalton's 60th birthday, to be held May 22-27, 2006 at Miami University in Oxford, Ohio (which is about 30 miles from Cincinnati, Ohio). We plan to emphasize the following themes: -- Nonlinear theory (Lipschitz classifications of Banach and metric spaces and related topics), -- Isomorphic theory of Banach spaces including connections with combinatorics and set theory, -- Algebraic and homological methods in Banach spaces, -- Approximation theory and algorithms in Banach spaces (greedy algorithms, interpolation etc.), -- Functional calculus and applications to Partial Differential Equations. The following people have agreed to be principal speakers at the conference: Yuri Brudnyi (Technion - Israel Institute of Technology, Israel) JesÃºs M. F. Castillo (University of Extremadura, Spain) Marianna CsÃ¶rnyei (University College, London, UK) Stephen Dilworth (University of South Carolina) Gilles Godefroy (UniversitÃ¨ Paris VI, France) William B. Johnson (Texas A&M University) Joram Lindenstrauss (Hebrew University, Israel) Assaf Naor (Microsoft Research) Edward Odell (University of Texas) Aleksander Pelczynski (Polish Academy of Sciences, Poland) David Preiss (University College, London, UK) Gideon Schechtman (Weizmann Institute of Science, Israel) Thomas Schlumprecht (Texas A&M University) Vladimir Temlyakov (University of South Carolina) Roman Vershynin (University of California - Davis) Lutz Weis (UniversitÃ¤t Karlsruhe, Germany) Przemyslaw Wojtaszczyk (Warsaw University, Poland) More information about the conference, its location, registration, accommodations and a printable poster are available at the website: http://www.users.muohio.edu/randrib/bsaa2006.html Please direct any questions to either of the organizers at randrib(a)muohio.edu or randrin(a)muohio.edu Sincerely yours, Beata Randrianantoanina Narcisse Randrianantoanina.

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Conference at Kent State
by Dale Alspach 16 Jan '05

16 Jan '05

A conference on Infinite Dimensional Analysis (IDAKent2005) will be held February 9-13, 2005, in honor of Richard Aron and Sean Dineen. The Conference web page is http://www.math.kent.edu/idaconf2005.html. We invite everyone, even those who cannot attend the conference, to send, as image files (preferably as JPG files), photographs of yourself with Richard and/or Sean, indicating the place and the year when they were taken. These photos will be displayed on the Conference web page. In order to arrange the schedule of the Conference we need to know who plans to give talks. The deadline for sending us the title and abstract of your talk is Friday, January 28 (and remember that everyone, absolutely everyone, is welcome whether or not he/she plans on giving a talk!) On the web page (LODGING), you can find information about many hotels from which to choose. To reserve hotel rooms at the IDA conference rate, please make your reservations through Misty Tackett. To do this, please (1) DOWNLOAD THE FORM FOR ROOM RESERVATIONS AS A TXT FILE, (2) FILL IN THIS FORM, and (3) E-MAIL THE FORM BACK TO Ms. Tackett at mtackett(a)math.kent.edu As an alternative, you can DOWNLOAD THE FORM FOR ROOM RESERVATIONS AS A PDF FILE, FILL IN THIS FORM, AND FAX IT BACK TO Ms. Tackett (++ 1 330 672 2209). Note that Adobe Reader 6 does not allow you to save what you write on the pdf, but you can print the modified pdf file. Reservations not made through Ms. Tackett will not be available at a reduced rate. The deadline for room reservations is Friday January 21st, 2005. Please let us know your arrival and departure times if you plan to fly to this area. We will arrange for a shuttle to take you to and from the airport when you are arriving or departing from the airports (Akron-Canton=CAK, Cleveland-Hopkins=CLE). To do this, we will need your detailed travel information. This will help us ensure that you are not missed at the airport if your flight happens to be delayed when arriving. By giving us your accurate departure information, we can help you be on time when going home as well! Please send the following information to garcia(a)math.kent.edu as soon as possible. On the web page you can also find in ARRIVALS AND DEPARTURES the following information that you can copy and paste into your email. Your Name: Arrival Information Airport (Cleveland or Akron): Flight Number: Arrival Date and Time: Departure Information Airport (Cleveland or Akron): Flight Number: Arrival Date and Time: By now a lot of people have confirmed that they will attend. Among them: Mar�a Acosta, University of Granada, Spain Raymundo Alencar, Instituto Tecnologico da Aeronautica, Sao Jose dos Campos, Brazil Richard Aron, Kent State University, USA Rajappa K. Asthagiri, Miami University, Middletown, USA Juan B�s, Bowling Green State University, USA Klaus Bierstedt, University of Paderborn, Germany Geraldo Botelho, Federal University of Uberl�ndia, Brazil Christopher Boyd, University College Dublin, Ireland Bernardo Cascales, University of Murcia, Spain Jes�s Castillo, University of Extremadura, Badajoz, Spain Yun Sung Choi, POSTECH, Pohang, Korea Joe Cima, The University of North Carolina at Chapel Hill, USA Antonio Roberto da Silva, Federal University of Rio de Janeiro, Brazil Andreas Defant, University of Oldenburg, Germany Joe Diestel, Kent State University, USA Ver�nica Dimant, University of San Andr�s, Victoria, Argentina Se�n Dineen, University College Dublin, Ireland Patrick Dowling, Miami University, Oxford, USA Maite Fern�ndez-Unzueta, CIMAT, Guadalajara, Mexico Jes�s Ferrer, University of Valencia, Spain Catherine Finet, University of Mons, Belgium Pablo Galindo, University of Valencia, Spain Domingo Garc�a, University of Valencia, Spain Bogdan Grecu, Tallaght Institute of Technology, Ireland Andr� Hallack, Federal University of Juiz de Fora, Brazil Lawrence A. Harris, University of Kentucky, USA Tatsuhiro Honda, Ariake National College of Technology, Fukuoka, Japan Remo H�gli, University College Dublin, Ireland Hans Jarchow, University of Zurich, Switzerland Jes�s Jaramillo, University Complutense of Madrid, Spain Ana Kaminska, The University of Memphis, USA Padraig Kirwan, Waterford Institue of Technology, Ireland Maciej Klimek, Uppsala University, Sweden Istvan Kovacs, Case Western Reserve University, Cleveland, USA L�szl� Lempert, Purdue University, USA Chris Lennard, University of Pittsburgh, USA Fernando Le�n, University of Cadiz, Spain Mikael Lindstr�m, �bo Akademi University, Finland Jos� L. G. Llavona, University Complutense of Madrid, Spain Lilian Louren�o, University of S�o Paulo, Brazil Michael Mackey, University College Dublin, Ireland Manuel Maestre, University of Valencia, Spain Miguel Mart�n, University of Granada, Spain F�lix Mart�nez Gim�nez, Technical University of Valencia, Spain Mieczyslaw Mastylo, Adam Mickiewicz University, Poznan, Poland Vicente Montesinos Santalucia, Technical University of Valencia, Spain Luiza Moraes, Federal University of Rio de Janeiro, Brazil Lawrence Narici, Saint Johns University, New York, USA Jos� Orihuela, University of Murcia, Spain Imre Patyi, Georgia State University, USA Aleksander Pelczynski, Institute of Mathematics, Polish Academy of Sciences, Poland Daniel Pellegrino, Federal University of Campina Grande, Brazil David P�rez, University Rey Juan Carlos of Madrid, Spain Alfredo Peris Manguillot, Technical University of Valencia, Spain Wieslaw Plesniak, Jagiellonian University, Krakow, Poland Lucas Quarta, University of Mons, Belgium Mar�a Jos� Rivera, Technical University of Valencia, Spain Pilar Rueda, University of Valencia, Spain Raymond Ryan, University of Galway, Ireland Jean Schmets, University of Li�ge, Belgium Pablo Sevilla, University of Valencia, Spain Emily Sprague, University of Wisconsin, USA Kondagunta Sundaresan, Cleveland State University, USA Ciaran Taylor, Tallaght Institute of Technology, Ireland Richard Timoney, Trinity College Dublin, Ireland Andrew Tonge, Kent State University, USA Milena Venkova, University College Dublin, Ireland Daniela Vieira, State University of Campinas, Brazil Ignacio Villanueva, University Complutense of Madrid, Spain Dietmar Vogt, University of Wuppertal, Germany Andriy Zagorodnyuk, Inst. for Applied Problems of Mechanics and Mathematics, Ukraine Ignacio Zalduendo, Universidad Torcuato di Tella, Buenos Aires, Argentina We hope that you too will be a participant in Kent during February 9 - 13, 2005! The organizing committee, Yun Sung Choi, Domingo Garc�a, Manolo Maestre, Andrew Tonge, Nacho Zalduendo.

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Abstract of a paper by A.G. Smirnov and M.A. Soloviev
by Dale Alspach 16 Jan '05

16 Jan '05

This is an announcement for the paper "On kernel theorems for Frechet and DF spaces" by A.G. Smirnov and M.A. Soloviev. Abstract: A convenient technique for calculating completed topological tensor products of functional Frechet or DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire analytic functions. Archive classification: Functional Analysis Mathematics Subject Classification: 46A32; 46E10; 46A04 Remarks: 10 pages The source file(s), kernel1.tex: 40782 bytes, is(are) stored in gzipped form as 0501187.gz with size 12kb. The corresponding postcript file has gzipped size 64kb. Submitted from: smirnov at lpi.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0501187 or http://arXiv.org/abs/math.FA/0501187 or by email in unzipped form by transmitting an empty message with subject line uget 0501187 or in gzipped form by using subject line get 0501187 to: math at arXiv.org.

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Abstract of a paper by W. T. Gowers
by Dale Alspach 16 Jan '05

16 Jan '05

This is an announcement for the paper "An infinite Ramsey theorem and some Banach-space dichotomies" by W. T. Gowers. Abstract: A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic nature which implies an interesting dichotomy for subspaces of Banach spaces. Combined with a result of Komorowski and Tomczak-Jaegermann, this gives a positive answer to Banach's problem. We then generalize the Ramsey-theoretic result and deduce a further dichotomy for Banach spaces with an unconditional basis. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20 (Primary) 03E02, 03E15, 05D10, 46B03 (Secondary) Citation: Ann. of Math. (2), Vol. 156 (2002), no. 3, 797--833 Remarks: 37 pages, published version The source file(s), ArxivGowers.tex: 109202 bytes, amltd2004.sty: 33983 bytes, is(are) stored in gzipped form as 0501105.tar.gz with size 42kb. The corresponding postcript file has gzipped size 112kb. Submitted from: wtg10 at dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0501105 or http://arXiv.org/abs/math.FA/0501105 or by email in unzipped form by transmitting an empty message with subject line uget 0501105 or in gzipped form by using subject line get 0501105 to: math at arXiv.org.

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