December 2008 - Banach - mathdept.okstate.edu

Abstract of a paper by Elisabeth Werner and Deping Ye
by alspach＠fourier.math.okstate.edu 29 Dec '08

29 Dec '08

This is an announcement for the paper "Inequalities for mixed $p$-affine surface area" by Elisabeth Werner and Deping Ye. Abstract: We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed $p$-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of $L_p$ affine surface areas, mixed $p$-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15 Remarks: 39 pages The source file(s), MixedLp.tex: 97032 bytes, is(are) stored in gzipped form as 0812.4550.gz with size 26kb. The corresponding postcript file has gzipped size 162kb. Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.4550 or http://arXiv.org/abs/0812.4550 or by email in unzipped form by transmitting an empty message with subject line uget 0812.4550 or in gzipped form by using subject line get 0812.4550 to: math(a)arXiv.org.

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Abstract of a paper by Kenneth R. Davidson and Alex Wright
by alspach＠fourier.math.okstate.edu 29 Dec '08

29 Dec '08

This is an announcement for the paper "Operator algebras with unique preduals" by Kenneth R. Davidson and Alex Wright. Abstract: We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak*-closed unital operator operator algebra containing a weak* dense subalgebra of compact operators has a unique Banach space predual. Archive classification: math.OA math.FA Mathematics Subject Classification: 47L50; 46B04; 47L35 Remarks: 13 pages The source file(s), DavidsonWright3a.tex: 44578 bytes, is(are) stored in gzipped form as 0812.3159.gz with size 14kb. The corresponding postcript file has gzipped size 96kb. Submitted from: krdavids(a)uwaterloo.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.3159 or http://arXiv.org/abs/0812.3159 or by email in unzipped form by transmitting an empty message with subject line uget 0812.3159 or in gzipped form by using subject line get 0812.3159 to: math(a)arXiv.org.

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Abstract of a paper by Roman Vershynin
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "Spectral norm of products of random and deterministic matrices" by Roman Vershynin. Abstract: We study the spectral norm of matrices M that can be factored as M=BA, where A is a random matrix with independent mean zero entries, and B is a fixed matrix. Under the (4+epsilon)-th moment assumption on the entries of A, we show that the spectral norm of such an m by n matrix M is bounded by \sqrt{m} + \sqrt{n}, which is sharp. In other words, in regard to the spectral norm, products of random and deterministic matrices behave similarly to random matrices with independent entries. This result along with the previous work of M. Rudelson and the author implies that the smallest singular value of a random m times n matrix with i.i.d. mean zero entries and bounded (4+epsilon)-th moment is bounded below by \sqrt{m} - \sqrt{n-1} with high probability. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52; 46B09 Remarks: 34 pages, no figures The source file(s), product-random-deterministic.tex: 81516 bytes, is(are) stored in gzipped form as 0812.2432.gz with size 22kb. The corresponding postcript file has gzipped size 147kb. Submitted from: romanv(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.2432 or http://arXiv.org/abs/0812.2432 or by email in unzipped form by transmitting an empty message with subject line uget 0812.2432 or in gzipped form by using subject line get 0812.2432 to: math(a)arXiv.org.

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Abstract of a paper by Robin Nittka
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "On a new type concept for Banach spaces" by Robin Nittka. Abstract: In order to measure qualitative properties we introduce a new notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. As an application we give a new proof that certain classical Banach spaces are non-isomorphic. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 7 pages The source file(s), type.bbl: 1571 bytes type.tex: 27062 bytes, is(are) stored in gzipped form as 0812.2216.tar.gz with size 9kb. The corresponding postcript file has gzipped size 75kb. Submitted from: robin.nittka(a)uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.2216 or http://arXiv.org/abs/0812.2216 or by email in unzipped form by transmitting an empty message with subject line uget 0812.2216 or in gzipped form by using subject line get 0812.2216 to: math(a)arXiv.org.

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Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "Factorization theorems for dominated polynomials" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However, this alternative scheme is shown not to be satisfactory until the equivalence is proved. Archive classification: math.FA Mathematics Subject Classification: 46G25 The source file(s), II-Factorization2dic08.tex: 15703 bytes, is(are) stored in gzipped form as 0812.1401.gz with size 5kb. The corresponding postcript file has gzipped size 62kb. Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.1401 or http://arXiv.org/abs/0812.1401 or by email in unzipped form by transmitting an empty message with subject line uget 0812.1401 or in gzipped form by using subject line get 0812.1401 to: math(a)arXiv.org.

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Abstract of a paper by Boris Rubin
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "Comparison of volumes of convex bodies in real, complex, and quaternionic spaces" by Boris Rubin. Abstract: The classical Busemann-Petty problem (1956) asks, whether origin-symmetric convex bodies in $\mathbb {R}^n$ with smaller hyperplane central sections necessarily have smaller volumes. It is known, that the answer is affirmative if $n\le 4$ and negative if $n>4$. The same question can be asked when volumes of hyperplane sections are replaced by more general comparison functions. We give unified exposition of this circle of problems in real, complex, and quaternionic $n$-dimensional spaces. All cases are treated simultaneously. In particular, we show that the Busemann-Petty problem in the quaternionic $n$-dimensional space has an affirmative answer if and only if $n =2$. The method relies on the properties of cosine transforms on the unit sphere. Possible generalizations for spaces over Clifford algebras are discussed. Archive classification: math.FA Mathematics Subject Classification: 44A12; 52A38 Remarks: 38 pages The source file(s), quaternion3.tex: 107627 bytes, is(are) stored in gzipped form as 0812.1300.gz with size 35kb. The corresponding postcript file has gzipped size 182kb. 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/0812.1300 or http://arXiv.org/abs/0812.1300 or by email in unzipped form by transmitting an empty message with subject line uget 0812.1300 or in gzipped form by using subject line get 0812.1300 to: math(a)arXiv.org.

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Abstract of a paper by R. J. Smith and S. Troyanski
by alspach＠fourier.math.okstate.edu 04 Dec '08

04 Dec '08

This is an announcement for the paper "Unconditional bases and strictly convex dual renormings" by R. J. Smith and S. Troyanski. Abstract: We present equivalent conditions for a space $X$ with an unconditional basis to admit an equivalent norm with a strictly convex dual norm. Archive classification: math.FA Mathematics Subject Classification: 46B03; 46B26; 46B15 The source file(s), unc_basis_dual_sc.tex: 45412 bytes, is(are) stored in gzipped form as 0811.4685.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: smith(a)math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.4685 or http://arXiv.org/abs/0811.4685 or by email in unzipped form by transmitting an empty message with subject line uget 0811.4685 or in gzipped form by using subject line get 0811.4685 to: math(a)arXiv.org.

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