Banach April 2011

banach@mathdept.okstate.edu

3 participants
21 discussions

Abstract of a paper by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel Gonzalez, and Yolanda Moreno
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "Banach spaces of universal disposition" by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel Gonzalez, and Yolanda Moreno. Abstract: In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\u{\i} space $\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\mathfrak F$ of finite dimensional spaces), or the Kubis space $\mathcal K$ (under {\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\mathfrak S$ of separable spaces). We moreover show that $\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\sf CH}-- it is isomorphic to an ultrapower of the Gurari\u{\i} space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties. Archive classification: math.FA Mathematics Subject Classification: 46A22, 46B04, 46B08, 46B26 Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.6065 or http://arXiv.org/abs/1103.6065

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Abstract of a paper by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel Gonzalez, and Yolanda Moreno
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "On separably injective Banach spaces" by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel Gonzalez, and Yolanda Moreno. Abstract: In this paper we deal with two weaker forms of injectivity which turn out to have a rich structure behind: separable injectivity and universal separable injectivity. We show several structural and stability properties of these classes of Banach spaces. We provide natural examples of (universally) separably injective spaces, including $\mathcal L_\infty$ ultraproducts built over countably incomplete ultrafilters, in spite of the fact that these ultraproducts are never injective. We obtain two fundamental characterizations of universally separably injective spaces: a) A Banach space $E$ is universally separably injective if and only if every separable subspace is contained in a copy of $\ell_\infty$ inside $E$. b) A Banach space $E$ is universally separably injective if and only if for every separable space $S$ one has $\Ext(\ell_\infty/S, E)=0$. The final Section of the paper focuses on special properties of $1$-separably injective spaces. Lindenstrauss\ obtained in the middle sixties a result that can be understood as a proof that, under the continuum hypothesis, $1$-separably injective spaces are $1$-universally separably injective; he left open the question in {\sf ZFC}. We construct a consistent example of a Banach space of type $C(K)$ which is $1$-separably injective but not $1$-universally separably injective. Archive classification: math.FA Mathematics Subject Classification: 46A22, 46B04, 46B08, 46A22, 46B04, 46B08, 46B26 Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.6064 or http://arXiv.org/abs/1103.6064

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International Conference AMAT 2012// New Book
by George A Anastassiou (ganastss) 28 Apr '11

28 Apr '11

Dear Colleague Hi! Two announcements you may be concerned: 1) Please find complete information about the International Conference on "Applied Mathematics and Approximation Theory 2012", to be held in Ankara, Turkey, May 17-19, 2012. So for all you need please visit: http://amat2012.etu.edu.tr/ For whatever you need please contact the organizer Professor Oktay Duman at oduman(a)etu.edu.tr<mailto:oduman@etu.edu.tr> please do not contact George Anastassiou. 2) May be your Library or you can order the new SPRINGER book-monograph by G. Anastassiou and O. Duman "Statistical Approximation Theory", (nothing to do with Statistics), all necessary information attached. Thank You for Your patience. I hope I see you in Ankara next year. Sincerely Yours George A. Anastassiou,Ph.D DOCTOR HONORIS CAUSA Professor of Mathematics Department of Mathematical Sciences The University of Memphis,Memphis,TN 38152,USA Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series: Concrete & Applicable Math. Springer Consultant-Editor in computational math books Birkhauser Consultant Editor in A.M.Sci. CRC-A.M. Advisor NOVA MATH books ADVISOR ganastss(a)memphis.edu http://www.eudoxuspress.com http://www.msci.memphis.edu/~ganastss/jocaaa http://www.msci.memphis.edu/~ganastss/jcaam http://www.msci.memphis.edu/~ganastss/jafa tel:(INT 001)- 901-678-3144 office 901-751-3553 home 901-678-2482 secr. Fax: 901-678-2480 Associate Editor in: J.Communications in Applied Analysis, Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO, J.Advances in non-linear Variational Inequalities, e-J.of Inequalities in Pure and Applied Math., Anals U.Oradea-Fasciola Mathematica, Journal of Inequalities and Applications, Inter.J.of Pure&Appl.Math.,MIA, Inter.J.of Computational and Numerical Analysis with Appl. President of world Soc.for study & promotion of Ancient Greek Mathematics. Honorary Editor Australian Journal of Mathematical Analysis and Appl. Panamerican Mathematical Journal Eudoxus Press,LLC Pres.

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Abstract of a paper by Michael Dore and Olga Maleva
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "A universal differentiability set in Banach spaces with separable dual" by Michael Dore and Olga Maleva. Abstract: We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fr\'echet differentiable somewhere in S. Archive classification: math.FA Remarks: 41 pages, 1 figure Submitted from: michael.j.dore(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.5094 or http://arXiv.org/abs/1103.5094

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Abstract of a paper by Christina Brech and Piotr Koszmider
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts" by Christina Brech and Piotr Koszmider. Abstract: For k being the first uncountable cardinal w_1 or k being the cardinality of the continuum c, we prove that it is consistent that there is no Banach space of density k in which it is possible to isomorphically embed every Banach space of the same density which has a uniformly G\^ateaux differentiable renorming or, equivalently, whose dual unit ball with the weak* topology is a subspace of a Hilbert space (a uniform Eberlein compact space). This complements a consequence of results of M. Bell and of M. Fabian, G. Godefroy, V. Zizler that assuming the continuum hypothesis, there is a universal space for all Banach spaces of density k=c=w_1 which have a uniformly G\^ateaux differentiable renorming. Our result implies, in particular, that \beta N-N may not map continuously onto a compact subset of a Hilbert space with the weak topology of density k=w_1 or k=c and that a C(K) space for some uniform Eberlein compact space K may not embed isomorphically into l_\infty/c_0. Archive classification: math.FA math.GN math.LO Mathematics Subject Classification: Primary 46B26, Secondary 03E35, 46B03 Submitted from: piotr.math(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.4259 or http://arXiv.org/abs/1103.4259

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Abstract of a paper by Oscar Blasco, Geraldo Botelho, Daniel Pellegrino and Pilar Rueda
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "On the interplay between different summability properties of multilinear mappings" by Oscar Blasco, Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this paper we establish profitable connections between different summability properties of multilinear mappings on Banach spaces, namely, multilinear mappings that are absolutely summing, almost summing, weakly summing and Cohen summing. For example, we give techniques to extend coincidence results from linear, bilinear and, in general, n-linear mappings to m-linear mappings for m larger than n. We do so by exploring the relationships between the summability properties of an n-linear mapping with those of its associated k-linear mappings, 1 <= k < n. We also provide an optimal generalization of recent results concerning inclusion theorems for absolutely summing multilinear mappings. Archive classification: math.FA Remarks: 27 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/1103.4040 or http://arXiv.org/abs/1103.4040

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Abstract of a paper by Guo TieXin and Zeng XiaoLin
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "An $L^{0}({\cal F},R)-$valued function's intermediate value theorem and its applications to random uniform convexity" by Guo TieXin and Zeng XiaoLin. Abstract: Let $(\Omega,{\cal F},P)$ be a probability space and $L^{0}({\cal F},R)$ the algebra of equivalence classes of real-valued random variables on $(\Omega,{\cal F},P)$. When $L^{0}({\cal F},R)$ is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from $L^{0}({\cal F},R)$ to $L^{0}({\cal F},R)$. As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module $(S,\|\cdot\|)$ is random uniformly convex iff $L^{p}(S)$ is uniformly convex for each fixed positive number $p$ such that $1<p<+\infty$. Archive classification: math.FA Mathematics Subject Classification: 46A22, 46B20, 46E30 Remarks: 14pages Submitted from: xlinzeng(a)ss.buaa.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.3775 or http://arXiv.org/abs/1103.3775

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Abstract of a paper by Luong Dang Ky
by alspach＠math.okstate.edu 11 Apr '11

11 Apr '11

This is an announcement for the paper "New Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators" by Luong Dang Ky. Abstract: We introduce a new class of Hardy spaces $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\'ia-Cuerva, Str\"omberg, and Torchinsky. Here, $\varphi: \mathbb R^n\times [0,\infty)\to [0,\infty)$ is a function such that $\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty$ weight. A function $f$ belongs to $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$ if and only if its maximal function $f^*$ is so that $x\mapsto \varphi(x,|f^*(x)|)$ is integrable. Such a space arises naturally for instance in the description of the product of functions in $H^1(\mathbb R^n)$ and $BMO(\mathbb R^n)$ respectively (see \cite{BGK}). We characterize these spaces via the grand maximal function and establish their atomic decomposition. We characterize also their dual spaces. The class of pointwise multipliers for $BMO(\mathbb R^n)$ characterized by Nakai and Yabuta can be seen as the dual of $L^1(\mathbb R^n)+ H^{\rm log}(\mathbb R^n)$ where $ H^{\rm log}(\mathbb R^n)$ is the Hardy space of Musielak-Orlicz type related to the Musielak-Orlicz function $\theta(x,t)=\displaystyle\frac{t}{\log(e+|x|)+ \log(e+t)}$. Furthermore, under additional assumption on $\varphi(\cdot,\cdot)$ we prove that if $T$ is a sublinear operator and maps all atoms into uniformly bounded elements of a quasi-Banach space $\mathcal B$, then $T$ uniquely extends to a bounded sublinear operator from $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$ to $\mathcal B$. These results are new even for the classical Hardy-Orlicz spaces on $\mathbb R^n$. Archive classification: math.CA math.FA Submitted from: dangky(a)math.cnrs.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.3757 or http://arXiv.org/abs/1103.3757

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Informal analysis seminar at Kent State (resend)
by Dale Alspach 07 Apr '11

07 Apr '11

Some information was omitted from the previous post. This is an announcement of a two-day long informal analysis seminar at Kent State which will be held next Thursday and Friday, April 14 and 15. More information about the schedule of talks is available at http://www.kent.edu/math/upload/informal-analysis-sem-announcement.pdf Richard M. Aron aron(a)math.kent.edu

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Informal analysis seminar at Kent State
by Dale Alspach 07 Apr '11

07 Apr '11

This is an announcement of an two-day long informal analysis seminar at Kent State which will be held next Thursday and Friday, April 14 and 15. Richard M. Aron aron(a)math.kent.edu

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Banach April 2011