Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Stefano Rossi
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "On a class of $C^*$ preduals of $l_1$" by Stefano Rossi. Abstract: Some nice preduals of $l_1$ are presented Archive classification: math.FA Remarks: 5 pages Submitted from: s-rossi(a)mat.uniroma1.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.4325 or http://arXiv.org/abs/1102.4325

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Abstract of a paper by Veronica Dimant and Silvia Lassalle
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "$M$-structures in vector-valued polynomial spaces" by Veronica Dimant and Silvia Lassalle. Abstract: This paper is concerned with the study of $M$-structures in spaces of polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether the class of weakly continuous on bounded sets $n$-homogeneous polynomials, $\mathcal P_w(^n E, F)$, is an $M$-ideal in the space of continuous $n$-homogeneous polynomials $\mathcal P(^n E, F)$. We show that there is some hope for this to happen only for a finite range of values of $n$. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when $E=\ell_p$ and $F=\ell_q$ or $F$ is a Lorentz sequence space $d(w,q)$. We extend to our setting the notion of property $(M)$ introduced by Kalton which allows us to lift $M$-structures from the linear to the vector-valued polynomial context. Also, when $\mathcal P_w(^n E, F)$ is an $M$-ideal in $\mathcal P(^n E, F)$ we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets. Archive classification: math.FA Mathematics Subject Classification: 47H60, 46B04, 47L22, 46B20 Submitted from: vero(a)udesa.edu.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.3850 or http://arXiv.org/abs/1102.3850

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Abstract of a paper by Franck Barthe, Chiara Bianchini, and Andrea Colesanti
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Isoperimetry and stability of hyperplanes for product probability measures" by Franck Barthe, Chiara Bianchini, and Andrea Colesanti. Abstract: We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure. Archive classification: math.FA math.PR Submitted from: chiara.bianchini(a)iecn.u-nancy.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.3621 or http://arXiv.org/abs/1102.3621

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Abstract of a paper by Guillaume Aubrun and Ion Nechita
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "The multiplicative property characterizes $\ell_p$ and $L_p$ norms" by Guillaume Aubrun and Ion Nechita. Abstract: We show that $\ell_p$ norms are characterized as the unique norms which are both invariant under coordinate permutation and multiplicative with respect to tensor products. Similarly, the $L_p$ norms are the unique rearrangement-invariant norms on a probability space such that $\|X Y\|=\|X\|\cdot\|Y\|$ for every pair $X,Y$ of independent random variables. Our proof relies on Cram\'er's large deviation theorem. Archive classification: math.FA Remarks: 8 pages, 1 figure Submitted from: inechita(a)uottawa.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.2618 or http://arXiv.org/abs/1102.2618

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Abstract of a paper by Daniel Fresen
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Comments on the floating body and the hyperplane conjecture" by Daniel Fresen. Abstract: We provide upper and lower bounds on the logarithmic Hausdorff distance between an arbitrary convex body $K\subset \mathbb{R}^{d}$\ and the convex floating body $K_{\delta }$ inside $K$. We also discuss the hyperplane conjecture (the slicing problem) and provide a reformulation of this famous unsolved mystery in terms of the floating body. Archive classification: math.FA math.PR Mathematics Subject Classification: 52A23, 52A20, 52A21, 52A38 Remarks: 8 pages Submitted from: djfb6b(a)mail.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.2570 or http://arXiv.org/abs/1102.2570

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Abstract of a paper by Daniel Pellegrino and Joilson Ribeiro
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "On everywhere almost summing multilinear operators" by Daniel Pellegrino and Joilson Ribeiro. Abstract: In this paper we obtain new results and characterizations for the classes (ideals) of everywhere almost summing multilinear operators and everywhere almost summing $n$-homogeneous polynomials. Among other results we prove that the ideal of everywhere almost summing polynomials is a global holomorphy type (this is not true for the original concept of almost summing polynomials). Archive classification: math.FA Remarks: 10 pages Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.1460 or http://arXiv.org/abs/1102.1460

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Abstract of a paper by Ralf Beckmann and Anton Deitmar
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Strong vector valued integrals" by Ralf Beckmann and Anton Deitmar. Abstract: Strong Bochner type integrals with values in locally convex spaces are introduced. It is shown that the strong integral exists in the same cases as the weak (Gelfand-Pettis) integral is known to exist. The strong integral has better continuity properties that the weak integral. Archive classification: math.FA Submitted from: deitmar(a)uni-tuebingen.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.1246 or http://arXiv.org/abs/1102.1246

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Abstract of a paper by Richard J. Smith
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Tree duplicates, $G_\delta$-diagonals and Gruenhage spaces" by Richard J. Smith. Abstract: We present an example in ZFC of a locally compact, scattered Hausdorff non-Gruenhage space $D$ having a $\G_delta$-diagonal. This answers a question posed by Orihuela, Troyanski and the author in a study of strictly convex norms on Banach spaces. In addition, we show that the Banach space of continuous functions $C_0(D)$ admits a $C^\infty$-smooth bump function. Archive classification: math.FA math.GN Submitted from: richard.smith(a)ucd.ie The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.0982 or http://arXiv.org/abs/1102.0982

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Abstract of a paper by Roman Vershynin
by alspach＠math.okstate.edu 04 Feb '11

04 Feb '11

This is an announcement for the paper "Invertibility of symmetric random matrices" by Roman Vershynin. Abstract: Let H be an n by n symmetric random matrix whose above-diagonal entries are general iid random variables (possibly discrete) with zero mean, unit variance, and subgaussian tail decay. We prove that H is singular with probability at most exp(n^{-c}) for some constant c>0, and that the spectral norm of the inverse of H is O(\sqrt{n}) with high probability. More generally, the spectrum of H is delocalized -- with high probability, there are no eigenvalues in an arbitrary fixed interval of the optimal length o(n^{-1/2}). The delocalization result also holds under the fourth moment assumption on the entries of H. These results improve upon the polynomial singularity bound O(n^{-1/8+epsilon}) due to Costello, Tao and Vu, and they generalize, up to constant factors, previous results for distributions whose first few moments match the moments of the normal distribution (due to the universality results of Tao and Vu) and for continuous distributions in the bulk of the spectrum (due to Erd\"os, Schlein and Yau). Archive classification: math.PR math.FA Mathematics Subject Classification: 15B52 Remarks: 52 pages Submitted from: romanv(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.0300 or http://arXiv.org/abs/1102.0300

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Abstract of a paper by Detelin Dosev, William B. Johnson, and Gideon Schechtman
by alspach＠math.okstate.edu 04 Feb '11

04 Feb '11

This is an announcement for the paper "Commutators on $L_p$, $1\le p<\infty$" by Detelin Dosev, William B. Johnson, and Gideon Schechtman. Abstract: The operators on $\LP=L_p[0,1]$, $1\leq p<\infty$, which are not commutators are those of the form $\lambda I + S$ where $\lambda\neq 0$ and $S$ belongs to the largest ideal in $\opLP$. The proof involves new structural results for operators on $\LP$ which are of independent interest. Archive classification: math.FA Mathematics Subject Classification: 47B47, 46E30 Submitted from: gideon(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.0137 or http://arXiv.org/abs/1102.0137

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