Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Guido Gherardi and Alberto Marcone
by alspach＠fourier.math.okstate.edu 13 Aug '08

13 Aug '08

This is an announcement for the paper "How much incomputable is the separable Hahn-Banach theorem?" by Guido Gherardi and Alberto Marcone. Abstract: We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak Konig's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibility for multi-valued functions, we obtain a computational counterpart of the subsystem of second order arithmetic WKL_0. We study analogies and differences between WKL_0 and the class of Sep-computable multi-valued functions. Extending work of Brattka, we show that a natural multi-valued function associated with the Hahn-Banach Extension Theorem is Sep-complete. Archive classification: math.LO math.FA Mathematics Subject Classification: 03F60 (Primary) 03B30, 46A22, 46S30 (Secondary) The source file(s), HahnBanach.tex: 106451 bytes, is(are) stored in gzipped form as 0808.1663.gz with size 32kb. The corresponding postcript file has gzipped size 149kb. Submitted from: alberto.marcone(a)dimi.uniud.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.1663 or http://arXiv.org/abs/0808.1663 or by email in unzipped form by transmitting an empty message with subject line uget 0808.1663 or in gzipped form by using subject line get 0808.1663 to: math(a)arXiv.org.

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Abstract of a paper by Pawel Mleczko
by alspach＠fourier.math.okstate.edu 13 Aug '08

13 Aug '08

This is an announcement for the paper "Compact multipliers on spaces of analytic functions" by Pawel Mleczko. Abstract: In the paper compact multiplier operators on Banach spaces of analytic functions on the unit disk with the range in Banach sequence lattices are studied. If the domain space $X$ is such that $H_\infty\hookrightarrow X\hookrightarrow H_1$, necessary and sufficient conditions for compactness are presented. Moreover, the calculation of the Hausdorff measure of noncompactness for diagonal operators between Banach sequence lattices is applied to obtaining the characterization of compact multipliers in case the domain space $X$ satisfies $H_\infty\hookrightarrow X\hookrightarrow H_2$. Archive classification: math.FA math.CV Mathematics Subject Classification: 42B15, 42B30, 46E05, 7B10 The source file(s), comp-multi.tex: 26131 bytes, is(are) stored in gzipped form as 0808.1359.gz with size 9kb. The corresponding postcript file has gzipped size 82kb. Submitted from: pml(a)amu.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.1359 or http://arXiv.org/abs/0808.1359 or by email in unzipped form by transmitting an empty message with subject line uget 0808.1359 or in gzipped form by using subject line get 0808.1359 to: math(a)arXiv.org.

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PLEASE POST
by George A Anastassiou (ganastss) 01 Aug '08

01 Aug '08

PLEASE POST "International Conference on Applied Mathematics and Approximation Theory 2008", October 11-13,2008, University of Memphis, Memphis, TN, USA (AMAT08). Plenary Speakers:A.Aldroubi, J.Bona, S.Dragomir, N.Govil, W.Han, M.J.Lai, H.Mhaskar, R.Mohapatra, G. N'Guerekata, B.Shekhtman, A.Zayed. Organizer:George Anastassiou, http://www.msci.memphis.edu/AMAT2008/ George A. Anastassiou,Ph.D DOCTOR HONORIS CAUSA Professor of Mathematics Department of Mathematical Sciences The University of Memphis,Memphis,TN 38152,USA Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series: Concrete & Applicable Math. Springer Consultant-Editor in computational math books Birkhauser Consultant Editor in A.M.Sci. CRC-A.M. Advisor NOVA MATH books ADVISOR ganastss(a)memphis.edu<mailto:ganastss@memphis.edu> http://www.eudoxuspress.com http://www.msci.memphis.edu/~ganastss/jocaaa http://www.msci.memphis.edu/~ganastss/jcaam http://www.msci.memphis.edu/~ganastss/jafa tel:(INT 001)- 901-678-3144 office 901-751-3553 home 901-678-2482 secr. Fax: 901-678-2480 Associate Editor in: J.Communications in Applied Analysis, Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO, J.Advances in non-linear Variational Inequalities, e-J.of Inequalities in Pure and Applied Math., Anals U.Oradea-Fasciola Mathematica, Journal of Inequalities and Applications, Inter.J.of Pure&Appl.Math.,MIA, Inter.J.of Computational and Numerical Analysis with Appl. President of World Soc.for study & promotion of Ancient Greek Mathematics Honorary Editor Australian Journal of Mathematical Analysis and Appl. Panamerican Mathematical Journal Eudoxus Press,LLC Pres.,ETC.

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Abstract of a paper by Daniel Carando, Veronica Dimant and Pablo Sevilla-Peris
by alspach＠fourier.math.okstate.edu 01 Aug '08

01 Aug '08

This is an announcement for the paper "Multilinear Holder-type inequalities on Lorentz sequence spaces" by Daniel Carando, Veronica Dimant and Pablo Sevilla-Peris. Abstract: We establish H\"older type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain estimates for their norms. We also consider norms of multilinear forms in different Banach multilinear ideals. Archive classification: math.FA Mathematics Subject Classification: 46A46, 46B45 The source file(s), CarandoDimantSevilla.tex: 59626 bytes, is(are) stored in gzipped form as 0807.4392.gz with size 18kb. The corresponding postcript file has gzipped size 122kb. Submitted from: dcarando(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.4392 or http://arXiv.org/abs/0807.4392 or by email in unzipped form by transmitting an empty message with subject line uget 0807.4392 or in gzipped form by using subject line get 0807.4392 to: math(a)arXiv.org.

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Abstract of a paper by Jesus Araujo and Luis Dubarbie
by alspach＠fourier.math.okstate.edu 01 Aug '08

01 Aug '08

This is an announcement for the paper "Biseparating maps between Lipschitz function spaces" by Jesus Araujo and Luis Dubarbie. Abstract: For complete metric spaces $X$ and $Y$, a description of linear biseparating maps between spaces of vector-valued Lipschitz functions defined on $X$ and $Y$ is provided. In particular it is proved that $X$ and $Y$ are bi-Lipschitz homeomorphic, and the automatic continuity of such maps is derived in some cases. Besides, these results are used to characterize the separating bijections between scalar-valued Lipschitz function spaces when $Y$ is compact. Archive classification: math.FA Mathematics Subject Classification: Primary 47B38; Secondary 46E40, 46H40, 47B33 Remarks: 17 pages; no figures The source file(s), lipschitz86.tex: 48992 bytes, is(are) stored in gzipped form as 0807.3835.gz with size 14kb. The corresponding postcript file has gzipped size 106kb. Submitted from: araujoj(a)unican.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.3835 or http://arXiv.org/abs/0807.3835 or by email in unzipped form by transmitting an empty message with subject line uget 0807.3835 or in gzipped form by using subject line get 0807.3835 to: math(a)arXiv.org.

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SUMIRFAS Schedule
by Dale Alspach 01 Aug '08

01 Aug '08

PDF version http://www.math.okstate.edu/~alspach/banach/IRFASschedule08.pdf SCHEDULE FOR SUMIRFAS 2008 The Informal Regional Functional Analysis Seminar August 8 - 10, 2008 Texas A&M University, College Station Talks for SUMIRFAS will also be posted on the Workshop in Analysis and Probability page: http://www.math.tamu.edu/research/workshops/linanalysis/ All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.tamu.edu/map/building/overview/BLOC.html Coffee and refreshments will be available in Blocker 155. The usual SUMIRFAS dinner will be on August 9. It will be a BBQ at the home of Jan and Bill Johnson. Julien Giol giol(a)math.tamu.edu, David Kerr (chair) kerr(a)math.tamu.edu, and Andrew Toms atoms(a)mathstat.yorku.ca are organizing a Concentration Week on “Operator Algebras, Dynamics, and Classification” which will take place August 4-8. For more information, go to http://www.math.tamu.edu/kerr/concweek08.html. We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cara to book your room, please tell them if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. For logistical support, please contact Cara Barton, cara(a)math.tamu.edu. For more infor- mation on the Workshop itself, please contact William Johnson, johnson(a)math.tamu.edu, David Larson, larson(a)math.tamu.edu, Gilles Pisier, pisier(a)math.tamu.edu, or Joel Zinn, jzinn(a)math.tamu.edu. Schedule for SUMIRFAS 2008 Friday, August 8 Blocker 165 1:40–2:10 Coffee & refreshments, Blocker 155 2:10–2:20 Greeting 2:20–3:10 Marius Dadarlat, “Finite dimensional approximations of amenable groups” 3:20–3:50 Constanze Liaw, “Singular integrals and rank one perturbations” 3:50–4:15 Coffee & refreshments, Blocker 155 4:15–5:05 Chris Phillips, “Freeness of actions of finite groups on C*-algebras” Saturday, August 9 Blocker 165 9:00–9:30 Coffee & refreshments, Blocker 155 9:30–10:20 Nate Brown, “Hilbert modules and the Cuntz semigroup” 10:30–11:00 Detelin Dosev, “Commutators on certain Banach spaces” 11:10–11:50 Grigoris Paouris, ”Small ball probability estimates for log-concave measures” 12:00–2:00 Lunch 2:00–3:00 Elisabeth Werner, “Orlicz functions and minima and maxima of random variables” 3:10–3:50 Bunyamin Sari, “On uniform classification of the direct sums of l_p -spaces” 3:50–4:10 Coffee & refreshments, Blocker 155 4:10–5:00 Timur Oikhberg, “The complexity of the complete isomorphism relation between subspaces of an operator space” 6:30– BBQ at Jan & Bill Johnson’s house, 1306 Deacon Dr., College Station, 979.696.2812 Please tell Cara, cara(a)math.tamu.edu, or Jaime,jaime(a)math.tamu.edu, if you (and spouse or companion, if applicable) will attend. Sunday, August 10 Blocker 165 9:30–10:00 Coffee & refreshments, Blocker 155 10:00–11:00 Bill Arveson, “Maximal vectors in Hilbert space and quantum entanglement” 11:15–12:15 Ron DeVore, “A Taste of Compressed Sensing”

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SUMIRFAS Schedule
by Bill Johnson 01 Aug '08

01 Aug '08

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Abstract of a paper by Alexey I. Popov and Vladimir G. Troitsky
by alspach＠fourier.math.okstate.edu 23 Jul '08

23 Jul '08

This is an announcement for the paper "A version of Lomonosov's theorem for collections of positive operators" by Alexey I. Popov and Vladimir G. Troitsky. Abstract: It is known that for every Banach space X and every proper WOT-closed subalgebra A of L(X), if A contains a compact operator then it is not transitive. That is, there exist non-zero x in X and f in X* such that f(Tx)=0 for all T in A. In the case of algebras of adjoint operators on a dual Banach space, V.Lomonosov extended this as follows: without having a compact operator in the algebra, |f(Tx)| is less than or equal to the essential norm of the pre-adjoint operator T_* for all T in A. In this paper, we prove a similar extension (in case of adjoint operators) of a result of R.Drnovsek. Namely, we prove that if C is a collection of positive adjoint operators on a Banach lattice X satisfying certain conditions, then there exist non-zero positive x in X and f in X* such that f(Tx) is less than or equal to the essential norm of T_* for all T in C. Archive classification: math.FA math.OA Mathematics Subject Classification: 47B65; 47A15 The source file(s), lom-drnov.tex: 31715 bytes, is(are) stored in gzipped form as 0807.3327.gz with size 10kb. The corresponding postcript file has gzipped size 86kb. Submitted from: vtroitsky(a)math.ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.3327 or http://arXiv.org/abs/0807.3327 or by email in unzipped form by transmitting an empty message with subject line uget 0807.3327 or in gzipped form by using subject line get 0807.3327 to: math(a)arXiv.org.

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Abstract of a paper by T. P. Hyt\"onen, J. L. Torrea, and D. V. Yakubovich
by alspach＠fourier.math.okstate.edu 23 Jul '08

23 Jul '08

This is an announcement for the paper "The Littlewood--Paley--Rubio de Francia property of a Banach space for the case of equal intervals" by T. P. Hyt\"onen, J. L. Torrea, and D. V. Yakubovich. Abstract: Let $X$ be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of $X$-valued functions holds true for all disjoint collections of subintervals of the set of integers of equal length and for all exponents $p$ greater or equal than 2 if and only if the space $X$ is a UMD space of type 2. The same criterion is obtained for the case of subintervals of the real line and Fourier integrals instead of Fourier series. Archive classification: math.FA Mathematics Subject Classification: 42Bxx; 46B20 Remarks: To appear in The Royal Society of Edinburgh Proc. A (Mathematics) The source file(s), lpr-equal_v6_arx.tex: 41797 bytes, is(are) stored in gzipped form as 0807.2981.gz with size 14kb. The corresponding postcript file has gzipped size 97kb. Submitted from: dmitry.yakubovich(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2981 or http://arXiv.org/abs/0807.2981 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2981 or in gzipped form by using subject line get 0807.2981 to: math(a)arXiv.org.

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Abstract of a paper by Hermann Pfitzner
by alspach＠fourier.math.okstate.edu 23 Jul '08

23 Jul '08

This is an announcement for the paper "Boundaries for Banach spaces determine weak compactness" by Hermann Pfitzner. Abstract: A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that boundary. Trivially, the pointwise convergence with respect to such a boundary is coarser than the weak topology on the Banach space. Godefroy's Boundary Problem asks whether nevertheless both topologies have the same bounded compact sets. This paper contains the answer in the positive. Archive classification: math.FA Mathematics Subject Classification: 46B20 The source file(s), boundary.tex: 30948 bytes, is(are) stored in gzipped form as 0807.2810.gz with size 10kb. The corresponding postcript file has gzipped size 76kb. Submitted from: Hermann.Pfitzner(a)univ-orleans.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2810 or http://arXiv.org/abs/0807.2810 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2810 or in gzipped form by using subject line get 0807.2810 to: math(a)arXiv.org.

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Banach