Banach January 2007

banach@mathdept.okstate.edu

1 participants
10 discussions

Abstract of a paper by Emanuel Milman
by Dale Alspach 30 Jan '07

30 Jan '07

This is an announcement for the paper "A solution to a question of A. Koldobsky" by Emanuel Milman. Abstract: In 2000, A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied by the author in [http://www.arxiv.org/math.MG/0512058], providing substantial positive evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprising negative answer to this question in a strong sense. This negative answer implies the existence of a non-trivial non-negative function in the range of the spherical Radon transform. Archive classification: Functional Analysis Remarks: 13 pages The source file(s), Solution-To-Koldobsky-Question.bbl: 5474 bytes, Solution-To-Koldobsky-Question.tex: 41825 bytes, is(are) stored in gzipped form as 0701779.tar.gz with size 14kb. The corresponding postcript file has gzipped size 110kb. Submitted from: emanuel.milman(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701779 or http://arXiv.org/abs/math.FA/0701779 or by email in unzipped form by transmitting an empty message with subject line uget 0701779 or in gzipped form by using subject line get 0701779 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge, Niels Jorgen Nielsen and Timur Oikhberg
by Dale Alspach 23 Jan '07

23 Jan '07

This is an announcement for the paper "Rosenthal operator spaces" by Marius Junge, Niels Jorgen Nielsen and Timur Oikhberg. Abstract: In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L_p-space, then it is either a script L_p-space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non--Hilbertian complemented operator subspaces of non commutative L_p-spaces and show that this class is much richer than in the commutative case. We investigate the local properties of some new classes of operator spaces for every $2<p< \infty$ which can be considered as operator space analogues of the Rosenthal sequence spaces from Banach space theory, constructed in 1970. Under the usual conditions on the defining sequence sigma we prove that most of these spaces are operator script L_p-spaces, not completely isomorphic to previously known such spaces. However it turns out that some column and row versions of our spaces are not operator script L_p-spaces and have a rather complicated local structure which implies that the Lindenstrauss--Rosenthal alternative does not carry over to the non-commutative case. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20;46L07;46L52 The source file(s), njnpart1new11.tex: 38162 bytes, njnpart2new11.tex: 48325 bytes, refnew11.tex: 4840 bytes, rosmatrixnew11.tex: 10401 bytes, uncomp2.tex: 6528 bytes, x3njn1111.tex: 5668 bytes, is(are) stored in gzipped form as 0701480.tar.gz with size 33kb. The corresponding postcript file has gzipped size 176kb. Submitted from: njn(a)imada.sdu.dk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701480 or http://arXiv.org/abs/math.FA/0701480 or by email in unzipped form by transmitting an empty message with subject line uget 0701480 or in gzipped form by using subject line get 0701480 to: math(a)arXiv.org.

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Abstract of a paper by Peter G. Casazza, Dan Edidin, Deepti Kalra and Vern I. Paulsen
by Dale Alspach 23 Jan '07

23 Jan '07

This is an announcement for the paper "Projections and the Kadison-Singer Problem" by Peter G. Casazza, Dan Edidin, Deepti Kalra and Vern I. Paulsen. Abstract: We prove some new equivalences of the paving conjecture and obtain some estimates on the paving constants. In addition we give a new family of counterexamples to one of the Akemann-Anderson conjectures. Archive classification: Functional Analysis Mathematics Subject Classification: 46L15; 47L25 The source file(s), 127.Projks.tex: 48714 bytes, is(are) stored in gzipped form as 0701450.gz with size 16kb. The corresponding postcript file has gzipped size 123kb. Submitted from: pete(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701450 or http://arXiv.org/abs/math.FA/0701450 or by email in unzipped form by transmitting an empty message with subject line uget 0701450 or in gzipped form by using subject line get 0701450 to: math(a)arXiv.org.

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Abstract of a paper by George Androulakis and Frank Sanacory
by Dale Alspach 16 Jan '07

16 Jan '07

This is an announcement for the paper "On the ``Multiple of the Inclusion Plus Compact'' problem" by George Androulakis and Frank Sanacory. Abstract: The ``multiple of the inclusion plus compact problem'' which was posed by T.W.~Gowers in 1996 and Th.~Schlumprecht in 2003, asks whether for every infinite dimensional Banach space $X$ there exists a closed subspace $Y$ of $X$ and a bounded linear operator from $Y$ to $X$ which is not a compact perturbation of a multiple of the inclusion map from $Y$ to $X$. We give sufficient conditions on the spreading models of seminormalized basic sequences of a Banach space $X$ which guarantee that the ``multiple of the inclusion plus compact'' problem has an affirmative answer for $X$. Our results strengthen a previous result of the first named author, E.~Odell, Th.~Schlumprecht and N.~Tomczak-Jaegermann as well as a result of Th.~Schlumprecht. We give an example of a Hereditarily Indecomposable Banach space where our results apply. For the proof of our main result we use an extension of E.~Odell's Schreier unconditionality result for arrays. Archive classification: Functional Analysis Mathematics Subject Classification: 46A32, 47B07 The source file(s), lambdaipluscpt.tex: 114786 bytes, is(are) stored in gzipped form as 0701354.gz with size 28kb. The corresponding postcript file has gzipped size 203kb. Submitted from: giorgis(a)math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701354 or http://arXiv.org/abs/math.FA/0701354 or by email in unzipped form by transmitting an empty message with subject line uget 0701354 or in gzipped form by using subject line get 0701354 to: math(a)arXiv.org.

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Abstract of a paper by E. Odell and Th. Schlumprecht
by Dale Alspach 12 Jan '07

12 Jan '07

This is an announcement for the paper "Embedding into Banach spaces with finite dimensional decompositions" by E. Odell and Th. Schlumprecht. Abstract: This paper deals with the following types of problems: Assume a Banach space $X$ has some property (P). Can it be embedded into some Banach space $Z$ with a finite dimensional decomposition having property (P), or more generally, having a property related to (P)? Secondly, given a class of Banach spaces, does there exist a Banach space in this class, or in a closely related one, which is universal for this class? Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; 46B20 Remarks: 26 pages The source file(s), os-embedding-final.tex: 109527 bytes, is(are) stored in gzipped form as 0701324.gz with size 33kb. The corresponding postcript file has gzipped size 182kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701324 or http://arXiv.org/abs/math.FA/0701324 or by email in unzipped form by transmitting an empty message with subject line uget 0701324 or in gzipped form by using subject line get 0701324 to: math(a)arXiv.org.

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Abstract of a paper by Boris Rubin
by Dale Alspach 12 Jan '07

12 Jan '07

This is an announcement for the paper "The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry" by Boris Rubin. Abstract: The lower dimensional Busemann-Petty problem asks, whether $n$-dimensional origin-symmetric convex bodies, having smaller $i$-dimensional sections, necessarily have smaller volumes. For $i=1$, the affirmative answer is obvious. For $i>3$, the answer is negative. For $i=2$ and $i=3$, the problem is still open, except when the body with smaller sections is a body of revolution. In this case the answer is affirmative. The paper contains a complete solution to the problem in the more general situation, when the body with smaller sections is invariant under orthogonal transformations preserving coordinate subspaces $R^{l}$ and $R^{n-l}$ of $R^{n}$ for arbitrary fixed $0<l<n$. Archive classification: Functional Analysis Mathematics Subject Classification: 44A12; 52A38 Remarks: 26 pages The source file(s), simplex2.tex: 72011 bytes, is(are) stored in gzipped form as 0701317.gz with size 23kb. The corresponding postcript file has gzipped size 155kb. Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701317 or http://arXiv.org/abs/math.FA/0701317 or by email in unzipped form by transmitting an empty message with subject line uget 0701317 or in gzipped form by using subject line get 0701317 to: math(a)arXiv.org.

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Abstract of a paper by Shachar Lovett and Sasha Sodin
by Dale Alspach 10 Jan '07

10 Jan '07

This is an announcement for the paper "Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits" by Shachar Lovett and Sasha Sodin. Abstract: It is well known that R^N has subspaces of dimension proportional to N on which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit constructions are known. Extending earlier work by Artstein--Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits. Archive classification: Functional Analysis; Metric Geometry; Probability Remarks: 16 pages The source file(s), derand.tex: 32081 bytes, is(are) stored in gzipped form as 0701102.gz with size 11kb. The corresponding postcript file has gzipped size 109kb. Submitted from: sodinale(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701102 or http://arXiv.org/abs/math.FA/0701102 or by email in unzipped form by transmitting an empty message with subject line uget 0701102 or in gzipped form by using subject line get 0701102 to: math(a)arXiv.org.

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Abstract of a paper by Peter G. Casazza and Janet C. Tremain
by Dale Alspach 10 Jan '07

10 Jan '07

This is an announcement for the paper "the paving conjecture is equivalent to the paving conjecture for triangular matrices" by Peter G. Casazza and Janet C. Tremain. Abstract: We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices. Archive classification: Functional Analysis Mathematics Subject Classification: 47A20, 47B99, 46B07 The source file(s), 12.5.06.tex: 20512 bytes, is(are) stored in gzipped form as 0701101.gz with size 7kb. The corresponding postcript file has gzipped size 87kb. Submitted from: pete(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701101 or http://arXiv.org/abs/math.FA/0701101 or by email in unzipped form by transmitting an empty message with subject line uget 0701101 or in gzipped form by using subject line get 0701101 to: math(a)arXiv.org.

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Abstract of a paper by J. Talponen
by Dale Alspach 02 Jan '07

02 Jan '07

This is an announcement for the paper "On weakly extremal structures in Banach spaces" by J. Talponen. Abstract: This paper deals with the interplay of the geometry of the norm and the weak topology in Banach spaces. Both dual and intrinsic connections between weak forms of rotundity and smoothness ared discussed. Weakly exposed points, weakly locally uniformly rotund spaces, smoothness, duality and the interplay of all the above are studied. An example of a Banach space, which is midpoint locally uniformly rotund but not weakly locally uniformly rotund is given. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 46A20 Remarks: 12 pages The source file(s), wg.tex: 45886 bytes, is(are) stored in gzipped form as 0701009.gz with size 13kb. The corresponding postcript file has gzipped size 103kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701009 or http://arXiv.org/abs/math.FA/0701009 or by email in unzipped form by transmitting an empty message with subject line uget 0701009 or in gzipped form by using subject line get 0701009 to: math(a)arXiv.org.

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Abstract of a paper by Bernhard Lamel
by Dale Alspach 02 Jan '07

02 Jan '07

This is an announcement for the paper "Local automorphisms of the Hilbert ball" by Bernhard Lamel. Abstract: We prove an analogue of Alexander's Theorem for holomorphic mappings of the unit ball in a complex Hilbert space: Every holomorphic mapping which takes a piece of the boundary of the unit ball into the boundary of the unit ball and whose differential at some point of this boundary is onto is the restriction of an automorphism of the ball. We also show that it is enough to assume that the mapping is only Gateaux-holomorphic. Archive classification: Complex Variables; Functional Analysis Mathematics Subject Classification: 32H12, 46G20, 46T25, 58C10 The source file(s), L_hilbertball/definitions.tex: 3255 bytes, L_hilbertball/hilbertball2.bbl: 1011 bytes, L_hilbertball/hilbertball2.tex: 24133 bytes, is(are) stored in gzipped form as 0612688.tar.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: bernhard.lamel(a)univie.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.CV/0612688 or http://arXiv.org/abs/math.CV/0612688 or by email in unzipped form by transmitting an empty message with subject line uget 0612688 or in gzipped form by using subject line get 0612688 to: math(a)arXiv.org.

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Banach January 2007