Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, and V.G. Troitsky
by Dale Alspach 20 Sep '05

20 Sep '05

This is an announcement for the paper "On norm closed ideals in L(\ell_p\oplus\ell_q)" by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, and V.G. Troitsky. Abstract: It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0 is the ideal of compact operators. The next natural question is to describe all closed ideals of L(\ell_p\oplus\ell_q) for 1 \le p,q < \infty, p \neq q, or, equivalently, the closed ideals in L(\ell_p,\ell_q) for p < q. This paper shows that for 1 < p < 2 < q < \infty there are at least four distinct proper closed ideals in L(\ell_p,\ell_q), including one that has not been studied before. The proofs use various methods from Banach space theory. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 47L20; 47B10; 47B37 Remarks: 24 pages 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/math.FA/0509414 or http://arXiv.org/abs/math.FA/0509414 or by email in unzipped form by transmitting an empty message with subject line uget 0509414 or in gzipped form by using subject line get 0509414 to: math(a)arXiv.org.

1 0

Abstract of a paper by Konstantin Boyko, Vladimir Kadets, Miguel Martin, and Dirk Werner
by Dale Alspach 17 Sep '05

17 Sep '05

This is an announcement for the paper "Numerical index and duality" by Konstantin Boyko, Vladimir Kadets, Miguel Martin, and Dirk Werner. Abstract: We present an example of a Banach space whose numerical index is strictly greater than the numerical index of its dual, giving a negative answer to a question which has been latent since the beginning of the seventies. We also show a particular case in which the numerical index of the space and the one of its dual coincide. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 47A12; 46B22; 46E15 The source file(s), miguelvovakostya.tex: 34653 bytes, is(are) stored in gzipped form as 0509374.gz with size 12kb. The corresponding postcript file has gzipped size 63kb. Submitted from: werner(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0509374 or http://arXiv.org/abs/math.FA/0509374 or by email in unzipped form by transmitting an empty message with subject line uget 0509374 or in gzipped form by using subject line get 0509374 to: math(a)arXiv.org.

1 0

Abstract of a paper by Yevgen Ivakhno, Vladimir Kadets and Dirk Werner
by Dale Alspach 17 Sep '05

17 Sep '05

This is an announcement for the paper "The Daugavet property for spaces of Lipschitz functions" by Yevgen Ivakhno, Vladimir Kadets and Dirk Werner. Abstract: For a compact metric space $K$ the space $\Lip(K)$ has the Daugavet property if and only if the norm of every $f \in \Lip(K)$ is attained locally. If $K$ is a subset of an $L_p$-space, $1<p<\infty$, this is equivalent to the convexity of~$K$. Archive classification: Functional Analysis Mathematics Subject Classification: 46B04; 46B25; 54E45 The source file(s), daugalip.tex: 46665 bytes, is(are) stored in gzipped form as 0509373.gz with size 15kb. The corresponding postcript file has gzipped size 75kb. Submitted from: werner(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0509373 or http://arXiv.org/abs/math.FA/0509373 or by email in unzipped form by transmitting an empty message with subject line uget 0509373 or in gzipped form by using subject line get 0509373 to: math(a)arXiv.org.

1 0

Abstract of a paper by Jan van Neerven
by Dale Alspach 16 Sep '05

16 Sep '05

This is an announcement for the paper "Separated sequences in uniformly convex Banach spaces" by Jan van Neerven. Abstract: We prove that the unit sphere of every infinite-dimensional uniformly convex Banach space with modulus of convexity $\delta$ contains a $(1+\frac12\delta(\frac23))$-separated sequence. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20 Citation: Colloq. Math. 102 (2005), 147-153 Remarks: 5 pages The source file(s), unif_convex.tex: 18207 bytes, is(are) stored in gzipped form as 0509344.gz with size 6kb. The corresponding postcript file has gzipped size 33kb. Submitted from: J.vanNeerven(a)math.tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0509344 or http://arXiv.org/abs/math.FA/0509344 or by email in unzipped form by transmitting an empty message with subject line uget 0509344 or in gzipped form by using subject line get 0509344 to: math(a)arXiv.org.

1 0

Abstract of a paper by Gilles Pisier
by Dale Alspach 16 Sep '05

16 Sep '05

This is an announcement for the paper "Remarks on $B(H)\otimes B(H)$" by Gilles Pisier. Abstract: We review the existing proofs that the min and max norms are different on $B(H)\otimes B(H)$ and give a shortcut avoiding the consideration of non-separable families of operator spaces. Archive classification: Operator Algebras; Functional Analysis Mathematics Subject Classification: 46L05, 46M05, 47D15 The source file(s), remarks.BB.tex: 17702 bytes, is(are) stored in gzipped form as 0509297.gz with size 7kb. The corresponding postcript file has gzipped size 43kb. Submitted from: gip(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0509297 or http://arXiv.org/abs/math.OA/0509297 or by email in unzipped form by transmitting an empty message with subject line uget 0509297 or in gzipped form by using subject line get 0509297 to: math(a)arXiv.org.

1 0

Abstract of a paper by Narcisse Randrianantoanina
by Dale Alspach 13 Sep '05

13 Sep '05

This is an announcement for the paper "Conditioned square functions for non-commutative martingales" by Narcisse Randrianantoanina. Abstract: We prove a weak-type (1,1) inequality involving conditioned square functions of martingales in non-commutative $L^p$-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the non-commutative Burkholder/Rosenthal inequalities from Ann. Proba. 31 (2003), 948-995. We also discuss BMO-norms of sums of non-commuting order independent operators. Archive classification: Functional Analysis; Probability Mathematics Subject Classification: 46L53; 60G42 Remarks: 38 pages The source file(s), condsquaref.tex: 107932 bytes, is(are) stored in gzipped form as 0509226.gz with size 31kb. The corresponding postcript file has gzipped size 136kb. Submitted from: randrin(a)muohio.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0509226 or http://arXiv.org/abs/math.FA/0509226 or by email in unzipped form by transmitting an empty message with subject line uget 0509226 or in gzipped form by using subject line get 0509226 to: math(a)arXiv.org.

1 0

Abstract of a paper by N. Brodskiy and D. Sonkin
by Dale Alspach 13 Sep '05

13 Sep '05

This is an announcement for the paper "Compression of uniform embeddings into Hilbert space" by N. Brodskiy and D. Sonkin. Abstract: If one tries to embed a metric space uniformly in Hilbert space, how close to quasi-isometric could the embedding be? We answer this question for finite dimensional CAT(0) cube complexes and for hyperbolic groups. In particular, we show that the Hilbert space compression of any hyperbolic group is 1. Archive classification: Group Theory; Functional Analysis; Geometric Topology Mathematics Subject Classification: 20F69; 20F65; 46C05 Remarks: 10 pages The source file(s), Uniform_Embeddings.tex: 27243 bytes, is(are) stored in gzipped form as 0509108.gz with size 9kb. The corresponding postcript file has gzipped size 50kb. Submitted from: brodskiy(a)math.utk.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.GR/0509108 or http://arXiv.org/abs/math.GR/0509108 or by email in unzipped form by transmitting an empty message with subject line uget 0509108 or in gzipped form by using subject line get 0509108 to: math(a)arXiv.org.

1 0

Abstract of a paper by S. J. Dilworth, E. Odell and B. Sari
by Dale Alspach 01 Sep '05

01 Sep '05

This is an announcement for the paper "Lattice structures and spreading models" by S. J. Dilworth, E. Odell and B. Sari. Abstract: We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices and countable lattices, and all finite lattices. Archive classification: Functional Analysis The source file(s), dos.tex: 60915 bytes, is(are) stored in gzipped form as 0508650.gz with size 19kb. The corresponding postcript file has gzipped size 88kb. Submitted from: bunyamin(a)unt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0508650 or http://arXiv.org/abs/math.FA/0508650 or by email in unzipped form by transmitting an empty message with subject line uget 0508650 or in gzipped form by using subject line get 0508650 to: math(a)arXiv.org.

1 0

Abstract of a paper by Mukul S. Patel
by Dale Alspach 30 Aug '05

30 Aug '05

This is an announcement for the paper "Noncommmutative Gelfand duality for not necessarily unital $C^*$-algebras, Jordan canonical form, and the existence of invariant subspaces" by Mukul S. Patel. Abstract: Gelfand-Naimark duality (Commutative $C^*$-algebras $\equiv$ Locally compact Hausdorff spaces) is extended to \begin{center}$C^*$-algebras $\equiv$ Quotient maps on locally compact Hausdorff spaces.\end{center} Using this duality, we give for an \emph{arbitrary} bounded operator on a complex Hilbert space of several dimensions, a functional calculus and the existence theorem for nontrivial invariant subspace. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46L05; 47A13; 47A13; 43A40; 22B05 Remarks: Under consideration for publication by Electronic Reasearch The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0508545 or http://arXiv.org/abs/math.FA/0508545 or by email in unzipped form by transmitting an empty message with subject line uget 0508545 or in gzipped form by using subject line get 0508545 to: math(a)arXiv.org.

1 0

Abstract of a paper by A K Mirmostafaee
by Dale Alspach 26 Aug '05

26 Aug '05

This is an announcement for the paper "A note on convex renorming and fragmentability" by A K Mirmostafaee. Abstract: Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a)~If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b)~If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c)~If the Banach space is weakly locally uniformly rotund, then its weak topology is fragmented by a metric which is stronger than the norm topology. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 54E99, 54H05 Citation: Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 2, May 2005, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0508311 or http://arXiv.org/abs/math.FA/0508311 or by email in unzipped form by transmitting an empty message with subject line uget 0508311 or in gzipped form by using subject line get 0508311 to: math(a)arXiv.org.

1 0

Jump to page:

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach