August 2011 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Diogo Diniz, G. A. Munoz-Fernandez, Daniel Pellegrino and J. B. Seoane-Sepulveda
by alspach＠math.okstate.edu 26 Aug '11

26 Aug '11

This is an announcement for the paper "The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal" by Diogo Diniz, G. A. Munoz-Fernandez, Daniel Pellegrino and J. B. Seoane-Sepulveda. Abstract: In this note we provide a family of constants, $C_{n}$, enjoying the Bohnenblust--Hille inequality and such that $\lim_{n\rightarrow\infty}C_{n}/C_{n-1}=1$, i.e., their asymptotic growth is the best possible. As a consequence, we also show that the optimal constants, $K_n$, in the Bohnenblust--Hille inequality have the best possible asymptotic behavior. Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1108.1550 or http://arXiv.org/abs/1108.1550

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Abstract of a paper by Stephen Sanchez
by alspach＠math.okstate.edu 26 Aug '11

26 Aug '11

This is an announcement for the paper "On the supremal $p$-negative type of a finite metric space" by Stephen Sanchez. Abstract: We study the supremal $p$-negative type of finite metric spaces. An explicit expression for the supremal $p$-negative type $\wp (X,d)$ of a finite metric space $(X,d)$ is given in terms its associated distance matrix, from which the supremal $p$-negative type of the space may be calculated. The method is then used to give a straightforward calculation of the supremal $p$-negative type of the complete bipartite graphs $K_{n,m}$ endowed with the usual path metric. A gap in the spectrum of possible supremal $p$-negative type values of path metric graphs is also proven. Archive classification: math.FA math.MG Mathematics Subject Classification: 51F99 (Primary) 46B85, 54E35 (Secondary) Remarks: 11 pages, 6 figures Submitted from: stephen.sanchez(a)unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1108.0451 or http://arXiv.org/abs/1108.0451

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Abstract of a paper by Yanqi Qiu
by alspach＠math.okstate.edu 26 Aug '11

26 Aug '11

This is an announcement for the paper "On the operator space $OUMD$ property for the column Hilbert space $C$" by Yanqi Qiu. Abstract: The operator space $OUMD$ property was introduced by Pisier in the context of verctor-valued noncommutative $L_p$-spaces. It is still unknown whether the property is independent of $p$ in this setting. In this paper, we prove that the column Hilbert space $C$ is $OUMD_p$ for all $1 < p < \infty$, this answers positively a question asked by Ruan. Archive classification: math.FA math.OA Submitted from: yqi.qiu(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.4941 or http://arXiv.org/abs/1107.4941

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Abstract of a paper by G. A. Munoz-Fernandez, D. Pellegrino and J. B. Seoane-Sepulveda
by alspach＠math.okstate.edu 26 Aug '11

26 Aug '11

This is an announcement for the paper "Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality" by G. A. Munoz-Fernandez, D. Pellegrino and J. B. Seoane-Sepulveda. Abstract: A classical inequality due to H.F. Bohnenblust and E. Hille states that for every positive integer $n$ there is a constant $C_{n}>0$ so that $$\left(\sum\limits_{i_{1},\dots,i_{n}=1}^{N}\left\vert U(e_{i_{^{1}}}, \dots ,e_{i_{n}})\right\vert^{\frac{2n}{n+1}}\right)^{\frac{n+1}{2n}}\leq C_{n}\left\Vert U\right\Vert$$ for every positive integer $N$ and every $n$-linear mapping $U:\ell_{\infty}^{N}\times\cdots\times\ell_{\infty}^{N}\rightarrow\mathbb{C}$. The original estimates for those constants from Bohnenblust and Hille are $$C_{n}=n^{\frac{n+1}{2n}}2^{\frac{n-1}{2}}.$$ In this note we present explicit formulae for quite better constants, and calculate the asymptotic behavior of these estimates, completing recent results of the second and third authors. For example, we show that, if $C_{\mathbb{R},n}$ and $C_{\mathbb{C},n}$ denote (respectively) these estimates for the real and complex Bohnenblust--Hille inequality then, for every even positive integer $n$, $$\frac{C_{\mathbb{R},n}}{\sqrt{\pi}} = \frac{C_{\mathbb{C},n}}{\sqrt{2}} = 2^{\frac{n+2}{8}}\cdot r_n$$ for a certain sequence $\{r_n\}$ which we estimate numerically to belong to the interval $(1,3/2)$ (the case $n$ odd is similar). Simultaneously, assuming that $\{r_n\}$ is in fact convergent, we also conclude that $$\displaystyle \lim_{n \rightarrow \infty} \frac{C_{\mathbb{R},n}}{C_{\mathbb{R},n-1}} = \displaystyle \lim_{n \rightarrow \infty} \frac{C_{\mathbb{C},n}}{C_{\mathbb{C},n-1}}= 2^{\frac{1}{8}}.$$ Archive classification: math.FA Remarks: 7 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/1107.4814 or http://arXiv.org/abs/1107.4814

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Abstract of a paper by Apostolos Giannopoulos, Grigoris Paouris, and Beatrice-Helen Vritsiou
by alspach＠math.okstate.edu 26 Aug '11

26 Aug '11

This is an announcement for the paper "A remark on the slicing problem" by Apostolos Giannopoulos, Grigoris Paouris, and Beatrice-Helen Vritsiou. Abstract: The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I_1(K,Z_q^o(K))=\int_K ||< : ,x> ||_{L_q(K)}dx. We show that an upper bound of the form I_1(K,Z_q^o(K))\leq C_1q^s\sqrt{n}L_K^2, with 1/2\leq s\leq 1, leads to the estimate L_n\leq \frac{C_2\sqrt[4]{n}log(n)} {q^{(1-s)/2}}, where L_n:= max {L_K : K is an isotropic convex body in R^n}. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A23, 46B06, 52A40 Remarks: 24 pages Submitted from: bevritsi(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.4527 or http://arXiv.org/abs/1107.4527

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Abstract of a paper by Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann
by alspach＠math.okstate.edu 26 Aug '11

26 Aug '11

This is an announcement for the paper "Chevet type inequality and norms of submatrices" by Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann. Abstract: We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of ``symmetric exponential" processes compared to the Gaussian ones in the Chevet inequality. This is used to give sharp upper estimate for a quantity $\Gamma_{k,m}$ that controls uniformly the Euclidean operator norm of the sub-matrices with $k$ rows and $m$ columns of an isotropic log-concave unconditional random matrix. We apply these estimates to give a sharp bound for the Restricted Isometry Constant of a random matrix with independent log-concave unconditional rows. We show also that our Chevet type inequality does not extend to general isotropic log-concave random matrices. Archive classification: math.PR math.FA math.MG Mathematics Subject Classification: Primary 52A23, 46B06, 46B09, 60E15 Secondary 15B52, 94B75 Submitted from: radamcz(a)mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.4066 or http://arXiv.org/abs/1107.4066

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Mathematics Lecturer position at University of Houston - Victoria
by Dale Alspach 24 Aug '11

24 Aug '11

The School of Arts and Sciences at the University of Houston - Victoria (UHV) invites applications for a Mathematics lecturer position starting in the Spring of 2012. We seek applicants preferably in the area of functional analysis, Banach Space Theory, Fixed Point theory. The starting date of the appointment is somewhat flexible, and we may accept applicants who are about to defend their PhD dissertation. The expected duties are mainly teaching four freshman courses per semester (Fall and Spring) and do service as well. The appointment is initially budgeted for one year, but is expected to last longer, renewed anually. Applicants should submit a letter of application, AMS cover sheet, CV, and have three letters of evaluation sent, preferably by email to teixeirar(a)uhv.edu. Applications received by October 15, 2011 will receive full consideration; applications will be accepted until the position is filled. UHV is a university with almost 5,000 students, located in Texas, 2 hours from major cities like Houston, Austin, San Antonio, Corpus Christi, and 3 hours from College Station. Most of the classes will have 25 or less students. Victoria is a city with almost 100 thousand people, with little of everything. We have applied people working in Computer Sciences, Biology and Statistics, and we are planning on strengthening the abstract Mathematics. UHV is committed to diversity and is an affirmative action, equal opportunity employer. Applications from women or minorities are especially encouraged. - ----------------------------------------------- Ricardo Verotti O. Teixeira School of Arts & Science University of Houston-Victoria http://www.ma.utexas.edu/users/rteixeira <http://www.ma.utexas.edu/users/rteixeira>

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Abstract of a paper by Grigoris Paouris and Elisabeth M. Werner
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "On the approximation of a polytope by its dual $L_{p}$-centroid bodies" by Grigoris Paouris and Elisabeth M. Werner. Abstract: We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P. In particular we show that if P has volume 1, lim_{p\rightarrow \infty} \frac{p}{\log{p}} \left( \frac{|Z_{p}^{\circ}(P)|}{|P^{\circ}|} -1 \right) = n^{2} . We provide an application to the approximation of polytopes by uniformly convex sets. Archive classification: math.FA 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/1107.3683 or http://arXiv.org/abs/1107.3683

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Abstract of a paper by Eliran Avni
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Calderon couples of p-convexified Banach lattices" by Eliran Avni. Abstract: We deal with the question of whether or not the p-convexified couple (X_0^{(p)},X_1^{(p)}) is a Calderon couple under the assumption that (X_0,X_1) is a Calderon couple of Banach lattices on some measure space. In this preliminary version of the paper we find that the answer is affirmative in the simple case where X_0 and X_1 are sequence spaces and an additional “positivity” assumption is imposed regarding (X_0,X_1). We also prove a quantitative version of the result with appropriate norm estimates. In future versions of this paper we plan to deal with other and more general cases of these results. Archive classification: math.FA Mathematics Subject Classification: 46B70, 46E30 Remarks: 7 pages Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.3238 or http://arXiv.org/abs/1107.3238

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