Banach April 2005

banach@mathdept.okstate.edu

5 participants
11 discussions

Abstract of a paper by Jan van Neerven and Mark Veraar
by Dale Alspach 25 Apr '05

25 Apr '05

This is an announcement for the paper "On the action of Lipschitz functions on vector-valued random sums" by Jan van Neerven and Mark Veraar. Abstract: Let $X$ be a Banach space and let $(\xi_j)_{j\ge 1}$ be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions are equivalent: (1). There exists a constant $K$ such that $$ \Bigl(\E\Big\|\sum_{j=1}^n \xi_j f(x_j)\Big\|^2\Bigr)^{\frac12} \leq K \n f\n_{\rm Lip} \Bigl(\E\Big\|\sum_{j=1}^n \xi_j x_j\Big\|^2\Bigr)^{\frac12} $$ for all Lipschitz functions $f:X\to X$ satisfying $f(0)=0$ and all finite sequences $x_1,\dots,x_n$ in $X$. (2). $X$ is isomorphic to a Hilbert space. Archive classification: Functional Analysis; Probability Mathematics Subject Classification: 46C15, 46B09, 47B10 Remarks: 8 pages, to appear in Archiv der Mathematik (Basel) The source file(s), lipschitzA.tex: 27762 bytes, is(are) stored in gzipped form as 0504452.gz with size 9kb. The corresponding postcript file has gzipped size 56kb. Submitted from: m.c.veraar(a)math.tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0504452 or http://arXiv.org/abs/math.FA/0504452 or by email in unzipped form by transmitting an empty message with subject line uget 0504452 or in gzipped form by using subject line get 0504452 to: math(a)arXiv.org.

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Vladimir Gurariy
by zvavitch＠math.kent.edu 19 Apr '05

19 Apr '05

It is with great sadness that the Department of Mathematical Sciences of Kent State University announces the passing of Dr. Vladimir Gurariy on Sunday, April 17, 2005. For many years, Vladimir was a colleague and great friend to all. We remember his brilliance in so many areas, his kindness and generosity, his sense of fun, and his humanity.

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Abstract of a paper by Florence Lancien, Beata Randrianantoanina, and Eric Ricard
by Dale Alspach 15 Apr '05

15 Apr '05

This is an announcement for the paper "On contractive projections in Hardy spaces" by Florence Lancien, Beata Randrianantoanina, and Eric Ricard. Abstract: We prove a conjecture of Wojtaszczyk that for $1\leq p<\infty$, $p\neq 2$, $H_p(\mathbbT)$ does not admit any norm one projections with dimension of the range finite and bigger than 1. This implies in particular that for $1\leq p<\infty$, $p\ne 2$, $H_p$ does not admit a Schauder basis with constant one. Archive classification: Functional Analysis; Complex Variables Remarks: 9 pages, to appear in Studia Mathematica The source file(s), hardy9.tex: 30622 bytes, is(are) stored in gzipped form as 0504294.gz with size 11kb. The corresponding postcript file has gzipped size 57kb. Submitted from: randrib(a)muohio.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0504294 or http://arXiv.org/abs/math.FA/0504294 or by email in unzipped form by transmitting an empty message with subject line uget 0504294 or in gzipped form by using subject line get 0504294 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge
by Dale Alspach 14 Apr '05

14 Apr '05

This is an announcement for the paper "Operator spaces and Araki-Woods factors" by Marius Junge. Abstract: We show that the operator Hilbert space OH introduced by Pisier embeds into the predual of the hyerfinite III1 factor. The main new tool is a Khintchine type inequality for the generators of the CAR algebra with respect to a quasi-free state. Our approach yields a Khintchine type inequality for the q-gaussian variables for all values q between -1 and 1. These results are closely related to recent results of Pisier and Shlyakhtenko in the free case. Archive classification: Operator Algebras; Functional Analysis Mathematics Subject Classification: 46L53, 47L25 The source file(s), carcomp.tex: 194521 bytes, is(are) stored in gzipped form as 0504255.gz with size 59kb. The corresponding postcript file has gzipped size 255kb. Submitted from: junge(a)math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0504255 or http://arXiv.org/abs/math.OA/0504255 or by email in unzipped form by transmitting an empty message with subject line uget 0504255 or in gzipped form by using subject line get 0504255 to: math(a)arXiv.org.

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Incorrect paper number for Inverse Limits and Function Algebras
by Dale Alspach 12 Apr '05

12 Apr '05

The announcement for the paper Inverse Limits and Function Algebras contains incorrect links such as http://front.math.ucdavis.edu/math.GN/0504228 The correct links are http://front.math.ucdavis.edu/math.GN/0504214 http://arXiv.org/abs/math.GN/0504214 Dale Alspach

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Abstract of a paper by Joan E. Hart and Kenneth Kunen
by Dale Alspach 12 Apr '05

12 Apr '05

This is an announcement for the paper "Inverse limits and function algebras" by Joan E. Hart and Kenneth Kunen. Abstract: Assuming Jensen's principle diamond, there is a compact Hausdorff space X which is hereditarily Lindelof, hereditarily separable, and connected, such that no closed subspace of X is both perfect and totally disconnected. The Proper Forcing Axiom implies that there is no such space. The diamond example also fails to satisfy the CSWP (the complex version of the Stone-Weierstrass Theorem). This space cannot contain the two earlier examples of failure of the CSWP, which were totally disconnected -- specifically, the Cantor set (W. Rudin) and beta N (Hoffman and Singer). Archive classification: General Topology; Functional Analysis Mathematics Subject Classification: 54D05; 46J10 Remarks: 16 pages The source file(s), invlim.tex: 45668 bytes, is(are) stored in gzipped form as 0504228.gz with size 15kb. The corresponding postcript file has gzipped size 80kb. Submitted from: kunen(a)math.wisc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.GN/0504228 or http://arXiv.org/abs/math.GN/0504228 or by email in unzipped form by transmitting an empty message with subject line uget 0504228 or in gzipped form by using subject line get 0504228 to: math(a)arXiv.org.

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Workshop at A&M
by Bill Johnson 11 Apr '05

11 Apr '05

Workshop in Linear Analysis and Probability Department of Mathematics Texas A&M University Summer 2005 The Summer 2005 session of the Workshop in Linear Analysis and Probability at Texas A&M University will be in session from July 5 until August 9. For information about the Workshop, consult the Workshop Home Page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 5-7. This year SUMIRFAS is dedicated to Haskell P. Rosenthal on the occasion of his retirement from the University of Texas at Austin. Haskell was one of the original organizers of UTAMIRFAS, the forerunner of SUMIRFAS. There will be a banquet in Haskell's honor on August 5. The usual SUMIRFAS dinner will be on August 6. Alvaro Arias, Edward Odell, and Thomas Schlumprecht are organizing a Haskell Fest Mini-Conference that will take place on August 4 and the morning of August 5. Ronald Douglas and Ciprian Foias are organizing a Mini-Conference on "Invariant and Hyperinvariant Subspaces - Old and New" that will take place August 8-9. This Mini-Conference is in honor of Carl Pearcy on the occasion of his 70th birthday. On August 8 there will be a banquet in Carl's honor. The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Mary Chapman (mary(a)math.tamu.edu). For more information 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). For information about the Haskell Fest Mini-Conference, please contact Alvaro Arias (aarias(a)math.du.edu), Edward Odell (odell(a)mail.ma.utexas.edu), or Thomas Schlumprecht (schlump(a)math.tamu.edu). For information about the Mini-Conference on Invariant Subspaces, please contact Ronald Douglas (rdouglas(a)math.tamu.edu).

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Abstract of a paper by Piotr Puchala
by Dale Alspach 11 Apr '05

11 Apr '05

This is an announcement for the paper "Continuous version of the Choquet Integral Reperesentation Theorem" by Piotr Puchala. Abstract: The Choquet - Bishop - de Leeuw theorem states that each element of a compact convex subset of a locally convex topological Hausdorff space is a barycenter of a probability measure supported by the set of extreme points of that set. By the Edgar - Mankiewicz result this remains true for nonempty closed bounded and convex set provided it has Radon - Nikodym property. In the paper it is shown, that Choquet - type theorem holds also for "moving" sets: they are values of a certain multifunction. Namely, the existence of a suitable weak* continuous family of probability measures "almost representing" points of such sets is proven. Both compact and noncompact cases are considered. The continuous versions of the Krein - Milman theorem are obtained as corollaries. Archive classification: Functional Analysis Mathematics Subject Classification: 54C60; 54C65; 46A55; 46B22 Citation: Studia Math. 168 (1), 2005, 15-24 Remarks: 9 pages, minor historical, editorial and bibliographical changes; The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0405217 or http://arXiv.org/abs/math.FA/0405217 or by email in unzipped form by transmitting an empty message with subject line uget 0405217 or in gzipped form by using subject line get 0405217 to: math(a)arXiv.org.

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Abstract of a paper by S. S. Kutateladze
by Dale Alspach 05 Apr '05

05 Apr '05

This is an announcement for the paper "On Grothendieck subspaces" by S. S. Kutateladze. Abstract: The modulus of an order bounded functional on a Riesz space is the sum of a pair of Riesz homomorphisms if and only if the kernel of this functional is a Grothendieck subspace of the ambient Riesz space. An operator version of this fact is given. Archive classification: Functional Analysis Mathematics Subject Classification: 46 B 42 The source file(s), sums.ams: 5318 bytes, is(are) stored in gzipped form as 0504046.gz with size 2kb. The corresponding postcript file has gzipped size 20kb. Submitted from: sskut(a)member.ams.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0504046 or http://arXiv.org/abs/math.FA/0504046 or by email in unzipped form by transmitting an empty message with subject line uget 0504046 or in gzipped form by using subject line get 0504046 to: math(a)arXiv.org.

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Abstract of a paper by Guillaume Aubrun and Stanislaw J. Szarek
by Dale Alspach 01 Apr '05

01 Apr '05

This is an announcement for the paper "Tensor products of convex sets and the volume of separable states on N qudits" by Guillaume Aubrun and Stanislaw J. Szarek. Abstract: This note deals with estimating the volume of the set of separable mixed quantum states when the dimension of the state space grows to infinity. This has been studied recently for qubits; here we consider larger particles. We also show that the partial transpose criterion becomes weaker when the dimension increases, and that the lower bound $6^{-N/2}$ on the (Hilbert-Schmidt) inradius of the set of separable states on $N$ qubits obtained recently by Gurvits and Barnum is essentially optimal. We employ standard tools of classical convexity, high-dimensional probability and geometry of Banach spaces; one relatively new point is a formal introduction of the concept of projective tensor products of convex bodies, and an initial study of this concept. PACS numbers: 03.65.Ud,03.67.-a,03.65.Db,02.40.Ft,02.50.Cw MSC-class: 46B28, 47B10, 47L05, 52A38, 81P68 Archive classification: Quantum Physics; Functional Analysis Remarks: 14 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/quant-ph/0503221 or http://arXiv.org/abs/quant-ph/0503221 or by email in unzipped form by transmitting an empty message with subject line uget 0503221 or in gzipped form by using subject line get 0503221 to: math(a)arXiv.org.

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Banach April 2005