July 2010 - 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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SUMIRFAS schedule
by Dale Alspach 22 Jul '10

22 Jul '10

Attachments are not normally allowed on messages to Banach. They are removed and stored on the server. The SUMIRFAS schedule that Bill Johnson sent out is available for viewing at http://cauchy.math.okstate.edu/pipermail/banach/attachments/20100721/6d4220… Dale Alspach

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SUMIRFAS schedule
by Bill Johnson 21 Jul '10

21 Jul '10

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Abstract of a paper by Qi Lu, Jiongmin Yong and Xu Zhang
by alspach＠fourier.math.okstate.edu 20 Jul '10

20 Jul '10

This is an announcement for the paper "Representation of Ito integrals by Lebesgue/Bochner integrals" by Qi Lu, Jiongmin Yong and Xu Zhang. Abstract: In [22], it was proved that as long as the integrand has certain properties, the corresponding It\^o integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later can be regarded as a variant of the classical Riesz Representation Theorem, and therefore it will be useful in studying other problems. Some remarkable consequences are presented as well, including a reasonable definition of exact controllability for stochastic differential equations and a condition which implies a Black-Scholes market to be complete. Archive classification: math.PR math.FA math.OC Remarks: 26pages Submitted from: xuzhang(a)amss.ac.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.2969 or http://arXiv.org/abs/1007.2969

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Abstract of a paper by Simon Luecking
by alspach＠fourier.math.okstate.edu 20 Jul '10

20 Jul '10

This is an announcement for the paper "Subspaces of almost Daugavet spaces" by Simon Luecking. Abstract: We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is: if $Z$ is a closed subspace of a separable almost Daugavet space $X$ such that the quotient space $X/Z$ contains no copy of $\ell_1$, then $Z$ has the almost Daugavet property, too. Archive classification: math.FA Mathematics Subject Classification: 46B04 Remarks: 5 pages Submitted from: simon.luecking(a)fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.2916 or http://arXiv.org/abs/1007.2916

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Abstract of a paper by Asuman Guven Aksoy and Grzegorz Lewicki
by alspach＠fourier.math.okstate.edu 20 Jul '10

20 Jul '10

This is an announcement for the paper "Minimal projections with respect to various norms" by Asuman Guven Aksoy and Grzegorz Lewicki. Abstract: We will show that a theorem of Rudin \cite{wr1}, \cite{wr}, permits us to determine minimal projections not only with respect to the operator norm but with respect to quasi-norms in operators ideals and numerical radius in many concrete cases. Archive classification: math.FA Remarks: 16 pages Submitted from: aaksoy(a)cmc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.2214 or http://arXiv.org/abs/1007.2214

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Abstract of a paper by Asuman Guven Aksoy and Grzegorz Lewicki
by alspach＠fourier.math.okstate.edu 20 Jul '10

20 Jul '10

This is an announcement for the paper "Best approximation in numerical radius" by Asuman Guven Aksoy and Grzegorz Lewicki. Abstract: Let $X$ be a reflexive Banach space. In this paper we give a necessary and sufficient condition for an operator $T\in \mathcal{K}(X)$ to have the best approximation in numerical radius from the convex subset $\mathcal{U} \subset \mathcal{K}(X),$ where $\mathcal{K}(X)$ denotes the set of all linear, compact operators from $X$ into $X.$ We will also present an application to minimal extensions with respect to the numerical radius. In particular some results on best approximation in norm will be generalized to the case of the numerical radius. Archive classification: math.FA Remarks: 13 pages Submitted from: aaksoy(a)cmc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.2205 or http://arXiv.org/abs/1007.2205

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Abstract of a paper by Maxim V. Balashov and Dusan Repovs
by alspach＠fourier.math.okstate.edu 14 Jul '10

14 Jul '10

This is an announcement for the paper "Weakly convex sets and modulus of nonconvexity" by Maxim V. Balashov and Dusan Repovs. Abstract: We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order. Using the new definition of the weakly convex set with the given modulus of nonconvexity we prove a new retraction theorem and we obtain new results about continuity of the intersection of two continuous set-valued mappings (one of which has nonconvex images) and new affirmative solutions of the splitting problem for selections. We also investigate relationship between the new definition and the definition of a proximally smooth set and a smooth set. Archive classification: math.FA math.GN Mathematics Subject Classification: 46A55, 52A01, 52A07, 54C60, 54C65 Citation: J. Math. Anal. Appl. 371:1 (2010), 113-127 Submitted from: dusan.repovs(a)guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.0162 or http://arXiv.org/abs/1007.0162

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Abstract of a paper by Mikhail Lifshits and Werner Linde
by alspach＠fourier.math.okstate.edu 14 Jul '10

14 Jul '10

This is an announcement for the paper "Compactness properties of weighted summation operators on trees" by Mikhail Lifshits and Werner Linde. Abstract: We investigate compactness properties of weighted summation operators $V_{\alpha,\sigma}$ as mapping from $\ell_1(T)$ into $\ell_q(T)$ for some $q\in (1,\infty)$. Those operators are defined by $$ (V_{\alpha,\sigma} x)(t) :=\alpha(t)\sum_{s\succeq t}\sigma(s) x(s)\,,\quad t\in T\;, $$ where $T$ is a tree with induced partial order $t \preceq s$ (or $s \succeq t$) for $t,s\in T$. Here $\alpha$ and $\sigma$ are given weights on $T$. We introduce a metric $d$ on $T$ such that compactness properties of $(T,d)$ imply two--sided estimates for $e_n(V_{\alpha,\sigma})$, the (dyadic) entropy numbers of $V_{\alpha,\sigma}$. The results are applied for concrete trees as e.g.~moderate increasing, biased or binary trees and for weights with $\alpha(t)\sigma(t)$ decreasing either polynomially or exponentially. We also give some probabilistic applications for Gaussian summation schemes on trees. Archive classification: math.FA Mathematics Subject Classification: Primary: 47B06, Secondary: 06A06, 05C05 Submitted from: lifts(a)mail.rcom.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.3867 or http://arXiv.org/abs/1006.3867

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Abstract of a paper by Taras Banakh and Robert Cauty
by alspach＠fourier.math.okstate.edu 14 Jul '10

14 Jul '10

This is an announcement for the paper "Topological classification of closed convex sets in Frechet spaces" by Taras Banakh and Robert Cauty. Abstract: We prove that each non-separable completely metrizable convex subset of a Frechet space is homeomorphic to a Hilbert space. This resolves an old (more than 30 years) problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowoslki and Torunczyk, this result implies that each closed convex subset of a Frechet space is homemorphic to $[0,1]^n\times [0,1)^m\times l_2(k)$ for some cardinals $0\le n\le\omega$, $0\le m\le 1$ and $k\ge 0$. Archive classification: math.FA math.GN math.GT Mathematics Subject Classification: 57N17, 46A04 Remarks: 8 pages Submitted from: tbanakh(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.3092 or http://arXiv.org/abs/1006.3092

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