June 2013 - 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 Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "Radon-Nikod\'ym property and thick families of geodesics" by Mikhail I. Ostrovskii. Abstract: Banach spaces without the Radon-Nikod\'ym property are characterized as spaces containing bilipschitz images of thick families of geodesics defined as follows. A family $T$ of geodesics joining points $u$ and $v$ in a metric space is called {\it thick} if there is $\alpha>0$ such that for every $g\in T$ and for any finite collection of points $r_1,\dots,r_n$ in the image of $g$, there is another $uv$-geodesic $\widetilde g\in T$ satisfying the conditions: $\widetilde g$ also passes through $r_1,\dots,r_n$, and, possibly, has some more common points with $g$. On the other hand, there is a finite collection of common points of $g$ and $\widetilde g$ which contains $r_1,\dots,r_n$ and is such that the sum of maximal deviations of the geodesics between these common points is at least $\alpha$. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B22, 46B85, 54E35 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.5807 or http://arXiv.org/abs/1306.5807

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Abstract of a paper by Gilles Pisier
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "On the metric entropy of the Banach-Mazur compactum" by Gilles Pisier. Abstract: We study of the metric entropy of the metric space $\cl B_n$ of all $n$-dimensional Banach spaces (the so-called Banach-Mazur compactum) equipped with the Banach-Mazur (multiplicative) ``distance" $d$. We are interested either in estimates independent of the dimension or in asymptotic estimates when the dimension tends to $\infty$. For instance, we prove that, if $N({\cl B_n},d, 1+\vp)$ is the smallest number of ``balls" of ``radius" $1+\vp$ that cover $\cl B_n$, then for any $\vp>0$ we have $$0<\liminf_{n\to \infty} \log\log N(\cl B_n,d,1+\vp)\le \limsup_{n\to \infty} \log\log N(\cl B_n,d,1+\vp)<\infty.$$ We also prove similar results for the matricial operator space analogues. Archive classification: math.FA 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/1306.5325 or http://arXiv.org/abs/1306.5325

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Abstract of a paper by Adam Marcus, Daniel A Spielman, and Nikhil Srivastava
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "Interlacing families II: Mixed characteristic polynomials and a question of Kadison and Singer" by Adam Marcus, Daniel A Spielman, and Nikhil Srivastava. Abstract: We use the method of interlacing families of polynomials to prove Weaver's conjecture KS_2, which is known to imply a positive answer to a famous question of Kadison and Singer via Anderson's Paving Conjecture. Our proof goes through an analysis of the largest roots of a family of polynomials that we call the "mixed characteristic polynomials" of a collection of matrices. Archive classification: math.CO math.FA math.OA Submitted from: spielman(a)cs.yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.3969 or http://arXiv.org/abs/1306.3969

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Abstract of a paper by Niushan Gao and Foivos Xanthos
by alspach＠math.okstate.edu 29 Jun '13

29 Jun '13

This is an announcement for the paper "Unbounded order convergence and application to martingales without probability" by Niushan Gao and Foivos Xanthos. Abstract: A net $(x_\alpha)_{\alpha\in \Gamma}$ in a vector lattice $X$ is unbounded order convergent (uo-convergent) to $x$ if $|x_\alpha-x| \wedge y \xrightarrow{{o}} 0$ for each $y \in X_+$, and is unbounded order Cauchy (uo-Cauchy) if the net $(x_\alpha-x_{\alpha'})_{\Gamma\times \Gamma}$ is uo-convergent to $0$. In the first part of this article, we study uo-convergent and uo-Cauchy nets in Banach lattices and use them to characterize Banach lattices with the positive Schur property and KB-spaces. In the second part, we use the concept of uo-Cauchy sequences to extend Doob's submartingale convergence theorems to a measure-free setting. Our results imply, in particular, that every norm bounded submartingale in $L_1(\Omega;F)$ is almost surely uo-Cauchy in $F$, where $F$ is an order continuous Banach lattice with a weak unit. Archive classification: math.FA Submitted from: foivos(a)ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.2563 or http://arXiv.org/abs/1306.2563

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Elton Lacey Funeral, Scholarship
by Dale Alspach 27 Jun '13

27 Jun '13

http://www.legacy.com/obituaries/theeagle/obituary.aspx?n=howard-lacey-elto… is a link to a newspaper obituary for Elton Lacey. It also gives details about the funeral. The family prefers donations to a scholarship fund rather than sending flowers. A link to a donation page is provided. Dale Alspach

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Dr. Howard Elton Lacey
by James Lacey 21 Jun '13

21 Jun '13

Just wanted to let the list know that my father Dr. Elton Lacey who was a Banach space researcher passed away today after a lengthy illness. Some of you may have known of him at the least. I have included a short summary of his life below. Thank you and best of luck to you all in your endeavors. Elton graduated from Leakey High School in 1955 and entered Texas A&M Univ. shortly thereafter. In the summer of 1957 he worked with the Corps of Engineers on the Mississippi river cutting transit lines for flood control projects. The first day there he went to the 4th St. Church of Christ and met his future wife Bonnie Brown and they were married August 1958 in Natchez, MS. That fall Elton continued his education at Abilene Christian Univ. where he received his B.A. in Mathematics in 1959 and his M.A. in Mathematics in 1960. Next Elton and Bonnie moved their family to Las Cruses, NM where Elton attended New Mexico State Univ. and earned his Ph.D. in Mathematics in 1963. In the summer of 1963 Elton worked at White Sands Missile Range in NM. That fall he returned to ACU as Assistant Professor. In the summer of 1964 he went to UT at Austin as an Asst. Professor. He was promoted to Assoc. Prof. in 1969 and full Prof. in 1974. He took leave from UT twice during his tenure. In the summer of 1966 and during the academic year of 1967-1968 Elton was at the Analysis Division of the Manned Space Craft Center. During the academic year of 1972-1973 Elton was at the Institute of Mathematics, Polish Academy of Science in Warsaw. While there Elton wrote letters home describing our experiences in Poland. His Aunt Cindy kept them and they were later typed up and turned into a family book. In 1974 he was promoted to Professor at UT Austin. When Dr. R. H. Bing returned to UT as Chairmen of Mathematics, Elton served as his Vice-Chairman. A number of his publications while at UT were with S. J. Bernau in Functional Analysis and Banach Spaces. He also published a book with Springer-Verlag, Berlin, NY in their prestigious Yellow Series, and another with UT Press and one with TAMU Press. In the summer of 1980 Elton taught math at the Free Univ. of Berlin, W. Germany. When he returned to Texas, he started as Prof. and Head of Mathematics, Texas A&M Univ., 1980-91. He served at Texas A&M Univ. from 1991-92 as Prof and Assoc. Dean. Later, he returned to his first love, teaching mathematics and retired in 2002. Upon retiring he was named a Prof. Emeritus of Mathematics. In the early 1990s Elton and Bonnie started working on family history. He was featured in the Dallas Morning News for using the internet for genealogy. Elton became an expert in Lacey family history and published several genealogy books including one on his maternal ancestors the Brices. He was a member of a number of heritage societies including the Sons of the American Revolution.

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Abstract of a paper by Miguel Martin
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Norm-attaining compact operators" by Miguel Martin. Abstract: We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. This is the negative answer to an open question posed in the 1970's. Actually, any strictly convex Banach space failing the approximation property serves as the range space. On the other hand, there are examples in which the domain space has Schauder basis. It now makes sense to discuss sufficient conditions on the domain or the range space to ensure that every compact linear operator between them can be approximated by norm attaining operators. We get several basic results in this line and mention some open problems. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B45, 46B28, 47B07 Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.1155 or http://arXiv.org/abs/1306.1155

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Abstract of a paper by Denis Potapov and Fedor Sukochev
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Frechet differentiability of Sp norms" by Denis Potapov and Fedor Sukochev. Abstract: One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts. We answer this question in the affirmative. A key technical observation underlying our proof is a discovery of connection between this question and recent affirmative resolution of L.S. Koplienko's conjecture concerning existence of higher order spectral shift functions. Archive classification: math.FA Submitted from: d.potapov(a)unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.0362 or http://arXiv.org/abs/1306.0362

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Abstract of a paper by Apostolos Giannopoulos, Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Geometry of the $L_q$-centroid bodies of an isotropic log-concave measure" by Apostolos Giannopoulos, Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou. Abstract: We study some geometric properties of the $L_q$-centroid bodies $Z_q(\mu )$ of an isotropic log-concave measure $\mu $ on ${\mathbb R}^n$. For any $2\ls q\ls\sqrt{n}$ and for $\varepsilon \in (\varepsilon_0(q,n),1)$ we determine the inradius of a random $(1-\varepsilon )n$-dimensional projection of $Z_q(\mu )$ up to a constant depending polynomially on $\varepsilon $. Using this fact we obtain estimates for the covering numbers $N(\sqrt{\smash[b]{q}}B_2^n,tZ_q(\mu ))$, $t\gr 1$, thus showing that $Z_q(\mu )$ is a $\beta $-regular convex body. As a consequence, we also get an upper bound for $M(Z_q(\mu ))$. Archive classification: math.FA math.MG Submitted from: apgiannop(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.0246 or http://arXiv.org/abs/1306.0246

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