Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Rishad Shahmurov
by alspach＠fourier.math.okstate.edu 19 Nov '08

19 Nov '08

This is an announcement for the paper "General Hormander and Mikhlin conditions for multipliers of Besov spaces" by Rishad Shahmurov. Abstract: Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hormander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equations are investigated. Archive classification: math.FA math.CA Mathematics Subject Classification: 34G10, 35J25, 35J70 Remarks: 16 The source file(s), FMTWeightedB.tex: 57462 bytes, is(are) stored in gzipped form as 0811.1350.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: shahmurov(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1350 or http://arXiv.org/abs/0811.1350 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1350 or in gzipped form by using subject line get 0811.1350 to: math(a)arXiv.org.

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Abstract of a paper by Vladimir Kadets, Miguel Martin, Javier Meri, and Rafael Paya
by alspach＠fourier.math.okstate.edu 10 Nov '08

10 Nov '08

This is an announcement for the paper "Convexity and smoothness of Banach spaces with numerical index one" by Vladimir Kadets, Miguel Martin, Javier Meri, and Rafael Paya . Abstract: We show that a Banach space with numerical index one cannot enjoy good convexity or smoothness properties unless it is one-dimensional. For instance, it has no WLUR points in its unit ball, its norm is not Frechet smooth and its dual norm is neither smooth nor strictly convex. Actually, these results also hold if the space has the (strictly weaker) alternative Daugavet property. We construct a (non-complete) strictly convex predual of an infinite-dimensional $L_1$ space (which satisfies a property called lushness which implies numerical index~$1$). On the other hand, we show that a lush real Banach space is neither strictly convex nor smooth, unless it is one-dimensional. In particular, if a subspace $X$ of the real space $C[0,1]$ is smooth or strictly convex, then $C[0,1]/X$ contains a copy of $C[0,1]$. Finally, we prove that the dual of any lush infinite-dimensional real space contains a copy of $\ell_1$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B04, 46B20, 47A12 Remarks: Illinois J. Math. (to appear) The source file(s), Kadets-Martin-Meri-Paya.tex: 61549 bytes, is(are) stored in gzipped form as 0811.0808.gz with size 19kb. The corresponding postcript file has gzipped size 120kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.0808 or http://arXiv.org/abs/0811.0808 or by email in unzipped form by transmitting an empty message with subject line uget 0811.0808 or in gzipped form by using subject line get 0811.0808 to: math(a)arXiv.org.

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Abstract of a paper by Piotr Koszmider, Miguel Martin, and Javier Meri
by alspach＠fourier.math.okstate.edu 10 Nov '08

10 Nov '08

This is an announcement for the paper "Extremely non-complex C(K) spaces" by Piotr Koszmider, Miguel Martin, and Javier Meri . Abstract: We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e.\ spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the positive Question 4.11 of [Kadets, Martin, Meri, Norm equalities for operators, \emph{Indiana U.\ Math.\ J.} \textbf{56} (2007), 2385--2411]. More concretely, we show that this is the case of some $C(K)$ spaces with few operators constructed in [Koszmider, Banach spaces of continuous functions with few operators, \emph{Math.\ Ann.} \textbf{330} (2004), 151--183] and [Plebanek, A construction of a Banach space $C(K)$ with few operators, \emph{Topology Appl.} \textbf{143} (2004), 217--239]. We also construct compact spaces $K_1$ and $K_2$ such that $C(K_1)$ and $C(K_2)$ are extremely non-complex, $C(K_1)$ contains a complemented copy of $C(2^\omega)$ and $C(K_2)$ contains a (1-complemented) isometric copy of $\ell_\infty$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B20, 47A99 Remarks: to appear in J. Math. Anal. Appl The source file(s), JMAA-07-3370R1.tex: 65250 bytes, is(are) stored in gzipped form as 0811.0577.gz with size 20kb. The corresponding postcript file has gzipped size 135kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.0577 or http://arXiv.org/abs/0811.0577 or by email in unzipped form by transmitting an empty message with subject line uget 0811.0577 or in gzipped form by using subject line get 0811.0577 to: math(a)arXiv.org.

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Abstract of a paper by G. Botelho, D. Diniz and D. Pellegrino
by alspach＠fourier.math.okstate.edu 10 Nov '08

10 Nov '08

This is an announcement for the paper "A note on lineability of sets of bounded non-absolutely summing operators" by G. Botelho, D. Diniz and D. Pellegrino. Abstract: In this note we sketch a method to prove that several sets of bounded non-absolutely p-summing operators are lineable. We partially solve a question posed by Puglisi and Seoane-Sepulveda on this subject. Archive classification: math.FA Mathematics Subject Classification: 47B10 Remarks: 4 pages The source file(s), lin5.tex: 10790 bytes, is(are) stored in gzipped form as 0811.0092.gz with size 4kb. The corresponding postcript file has gzipped size 52kb. Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.0092 or http://arXiv.org/abs/0811.0092 or by email in unzipped form by transmitting an empty message with subject line uget 0811.0092 or in gzipped form by using subject line get 0811.0092 to: math(a)arXiv.org.

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Position at University of Wisconsin-Eau Claire
by Tong, Simei 06 Nov '08

06 Nov '08

Department of Mathematics University of Wisconsin-Eau Claire A probationary tenure-track faculty position is available in the Department of Mathematics at the rank of Assistant Professor beginning August 24, 2009. See http://www.uwec.edu/acadaff/jobs/faculty/MathF-537.htm for further details.

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Banach Journal of Mathematical Analysis
by Dale Alspach 04 Nov '08

04 Nov '08

Please consider submitting papers to the Banach Journal of Mathematical Analysis. A poster for the journal can be viewed at http://www.emis.de/journals/BJMA/Poster_BJMA.pdf Banach Journal of Mathematical Analysis (BJMA) is an international and peer-reviewed electronic journal presenting papers on functional analysis, operator theory and related topics. The journal focuses on (but is not limited to) Hilbert spaces, normed spaces, normed algebras, normed modules, operator algebras, operator spaces, topological algebras, homology of Banach algebras, linear operators, matrix analysis, norm and operator inequalities, normed aspects of functional equations, stability of functional equations, approximation theory, harmonic analysis, Fourier analysis, spectral theory and non-commutative geometry. The journal is composed of original research and survey articles. Additional information is available at http://www.emis.de/journals/BJMA/ ********************************************** Mohammad Sal Moslehian Ph.D., Professor of Mathematics Address: Dept. of Pure Math., P.O. Box 1159 Ferdowsi University of Mashhad Mashhad 91775, Iran E-mails: moslehian(a)ams.org moslehian(a)um.ac.ir Home: http://www.um.ac.ir/~moslehian/ **********************************************

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Abstract of a paper by R. Fry and L. Keener
by alspach＠fourier.math.okstate.edu 04 Nov '08

04 Nov '08

This is an announcement for the paper "Approximation by Lipschitz, analytic maps on certain Banach spaces" by R. Fry and L. Keener. Abstract: We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 19 pages The source file(s), FryKeenerv2.tex: 58919 bytes, is(are) stored in gzipped form as 0810.5600.gz with size 15kb. The corresponding postcript file has gzipped size 111kb. Submitted from: rfry(a)tru.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.5600 or http://arXiv.org/abs/0810.5600 or by email in unzipped form by transmitting an empty message with subject line uget 0810.5600 or in gzipped form by using subject line get 0810.5600 to: math(a)arXiv.org.

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Abstract of a paper by Gianluca Cassese
by alspach＠fourier.math.okstate.edu 04 Nov '08

04 Nov '08

This is an announcement for the paper "Sure wins, separating probabilities and the representation of linear functionals" by Gianluca Cassese. Abstract: We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions Archive classification: math.FA math.PR Mathematics Subject Classification: 28A25, 28C05 The source file(s), JMAAR1.tex: 32542 bytes, is(are) stored in gzipped form as 0709.3411.gz with size 11kb. The corresponding postcript file has gzipped size 283kb. Submitted from: g.cassese(a)economia.unile.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0709.3411 or http://arXiv.org/abs/0709.3411 or by email in unzipped form by transmitting an empty message with subject line uget 0709.3411 or in gzipped form by using subject line get 0709.3411 to: math(a)arXiv.org.

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Abstract of a paper by Gilles Pisier
by alspach＠fourier.math.okstate.edu 04 Nov '08

04 Nov '08

This is an announcement for the paper "Remarks on the non-commutative Khintchine inequalities for $0<p<2$" by Gilles Pisier. Abstract: We show that the validity of the non-commutative Khintchine inequality for some $q$ with $1<q<2$ implies its validity (with another constant) for all $1\le p<q$. We prove this for the inequality involving the Rademacher functions, but also for more general ``lacunary'' sequences, or even non-commutative analogues of the Rademacher functions. For instance, we may apply it to the ``$Z(2)$-sequences'' previously considered by Harcharras. The result appears to be new in that case. It implies that the space $\ell^n_1$ contains (as an operator space) a large subspace uniformly isomorphic (as an operator space) to $R_k+C_k$ with $k\sim n^{\frac12}$. This naturally raises several interesting questions concerning the best possible such $k$. Unfortunately we cannot settle the validity of the non-commutative Khintchine inequality for $0<p<1$ but we can prove several would be corollaries. For instance, given an infinite scalar matrix $[x_{ij}]$, we give a necessary and sufficient condition for $[\pm x_{ij}]$ to be in the Schatten class $S_p$ for almost all (independent) choices of signs $\pm 1$. We also characterize the bounded Schur multipliers from $S_2$ to $S_p$. The latter two characterizations extend to $0<p<1$ results already known for $1\le p\le2$. In addition, we observe that the hypercontractive inequalities, proved by Carlen and Lieb for the Fermionic case, remain valid for operator space valued functions, and hence the Kahane inequalities are valid in this setting. Archive classification: math.OA math.FA The source file(s), Remarks-Khintchine.Oct24.tex: 85759 bytes, is(are) stored in gzipped form as 0810.5705.gz with size 26kb. The corresponding postcript file has gzipped size 175kb. Submitted from: pisier(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.5705 or http://arXiv.org/abs/0810.5705 or by email in unzipped form by transmitting an empty message with subject line uget 0810.5705 or in gzipped form by using subject line get 0810.5705 to: math(a)arXiv.org.

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Abstract of a paper by Christian Rosendal
by alspach＠fourier.math.okstate.edu 04 Nov '08

04 Nov '08

This is an announcement for the paper "Infinite asymptotic games" by Christian Rosendal. Abstract: We study infinite asymptotic games in Banach spaces with an F.D.D. and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into $\ell_p$ sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. These results are related to questions of rapidity of subsequence extraction from normalised weakly null sequences. Archive classification: math.FA math.LO Mathematics Subject Classification: Primary: 46B03, Secondary 03E15 The source file(s), AsymptoticGames42.tex: 71838 bytes, is(are) stored in gzipped form as 0608616.gz with size 22kb. The corresponding postcript file has gzipped size 0kb. Submitted from: rosendal(a)math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math/0608616 or http://arXiv.org/abs/math/0608616 or by email in unzipped form by transmitting an empty message with subject line uget math/0608616 or in gzipped form by using subject line get math/0608616 to: math(a)arXiv.org.

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