Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Lingxin Bao, Lixin Cheng, Qingjin Cheng and Duanxu Dai
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "On universally-left-stability of Banach spaces for $\varepsilon$-isometries" by Lingxin Bao, Lixin Cheng, Qingjin Cheng and Duanxu Dai. Abstract: Let $X$, $Y$ be two real Banach spaces, and $\eps\geq0$. A map $f:X\rightarrow Y$ is said to be a standard $\eps$-isometry if $|\|f(x)-f(y)\|-\|x-y\||\leq\eps$ for all $x,y\in X$ and with $f(0)=0$. We say that a pair of Banach spaces $(X,Y)$ is stable if there exists $\gamma>0$ such that for every such $\eps$ and every standard $\eps$-isometry $f:X\rightarrow Y$ there is a bounded linear operator $T:L(f)\equiv\overline{{\rm span}}f(X)\rightarrow X$ such that $\|Tf(x)-x\|\leq\gamma\eps$ for all $x\in X$. $X (Y)$ is said to be left (right)-universally stable, if $(X,Y)$ is always stable for every $Y (X)$. In this paper, we show that if a dual Banach space $X$ is universally-left-stable, then it is isometric to a complemented $w^*$-closed subspace of $\ell_\infty(\Gamma)$ for some set $\Gamma$, hence, an injective space; and that a Banach space is universally-left-stable if and only if it is a cardinality injective space. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B20, 47A58 (Primary) 26E25, 46A20, 46A24 (Secondary) Remarks: 10 pages, submitted to Acta Mathematica Sinica, English Series Submitted from: dduanxu(a)163.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.3656 or http://arXiv.org/abs/1301.3656

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Abstract of a paper by Patrick J. Rabier
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "Differentiability of quasiconvex functions on separable Banach spaces" by Patrick J. Rabier. Abstract: We investigate the differentiability properties of real-valued quasiconvex functions f defined on a separable Banach space X. Continuity is only assumed to hold at the points of a dense subset. If so, this subset is automatically residual. Sample results that can be quoted without involving any new concept or nomenclature are as follows: (i) If f is usc or strictly quasiconvex, then f is Hadamard differentiable at the points of a dense subset of X (ii) If f is even, then f is continuous and Gateaux differentiable at the points of a dense subset of X. In (i) or (ii), the dense subset need not be residual but, if X is also reflexive, it contains the complement of a Haar null set. Furthermore, (ii) remains true without the evenness requirement if the definition of Gateaux differentiability is generalized in an unusual, but ultimately natural, way. The full results are much more general and substantially stronger. In particular, they incorporate the well known theorem of Crouzeix, to the effect that every real-valued quasiconvex function on R^N is Frechet differentiable a.e. Archive classification: math.OC math.FA Submitted from: rabier(a)imap.pitt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.2852 or http://arXiv.org/abs/1301.2852

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Abstract of a paper by Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "Affine invariant points" by Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner. Abstract: We answer in the negative a question by Gruenbaum who asked if there exists a finite basis of affine invariant points. We give a positive answer to another question by Gruenbaum about the "size" of the set of all affine invariant points. Related, we show that the set of all convex bodies K, for which the set of affine invariant points is all of n-dimensional Euclidean space, is dense in the set of convex bodies. Crucial to establish these results, are new affine invariant points, not previously considered in the literature. 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/1301.2606 or http://arXiv.org/abs/1301.2606

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Abstract of a paper by Mark Rudelson
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "Lecture notes on non-asymptotic theory of random matrices" by Mark Rudelson. Abstract: We discuss recent developments in the study of the spectral properties of random matrices of a large fixed size, concentrating on the extreme singular values. Bounds for the extreme singular values were crucial in establishing several limit laws of random matrix theory. Besides the random matrix theory itself, these bounds have applications in geometric functional analysis and computer science. Archive classification: math.PR math.FA Mathematics Subject Classification: 60B20 Remarks: Lecture notes from the AMS short course on random matrices, 44 Submitted from: rudelson(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.2382 or http://arXiv.org/abs/1301.2382

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Abstract of a paper by Hossein Dehghan
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "A characterization of inner product spaces related to the distance" by Hossein Dehghan. Abstract: A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance. Archive classification: math.FA Remarks: To appear in Math. Notes Submitted from: h_dehghan(a)iasbs.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.1001 or http://arXiv.org/abs/1301.1001

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announcement
by Gonzalez Ortiz, Manuel 22 Jan '13

22 Jan '13

ANNOUNCEMENT OF MEETING Operators on Banach spaces -an homage to Pietro Aiena C.I.E.M., Castro Urdiales (Cantabria, Spain), 10th–14th June 2013 Operator theory is the research field of Professor Pietro Aiena, to whom this meeting pays a well-deserved homage. INVITED SPEAKERS José Bonet (Universidad Politécnica de Valencia) Cristina Câmara (Universidade Técnica de Lisboa) Gustavo Corach (Instituto Argentino de Matemática) Robin Harte (Trinity College Dublin) Francisco L. Hernández (Universidad Complutense de Madrid) Teresa Malheiro (Universidade do Minho) Martin Mathieu (Queen's University Belfast) Alfonso Montes (Universidad de Sevilla) Vladimír Müller (Czech Academy of Sciences) Matthias Neufang (Université Lille 1) Florian Vasilescu (Université Lille 1) ORGANIZATION Jesús M. F. Castillo (Universidad de Extremadura) Manuel González Ortiz (Universidad de Cantabria) Mostafa Mbekhta (Université Lille 1) Camillo Trapani (Università degli studi di Palermo) Registration and additional information http://www.ciem.unican.es/encuentros/banach/2013/

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A Celebration of The Life of Ted Odell
by Dale Alspach 14 Jan '13

14 Jan '13

There will be "A Celebration of The Life of Ted Odell" on Saturday January 19th at 3:30pm on campus in the Main Tower (Room number MAI 212). Following the celebration, Ted's family have invited people to attend a buffet reception starting at 6pm at The Green Pastures. So that the family can get a rough idea of the number of people, if you think that you (and your guests) will attend the reception please email Linda Porras with the number (lind(a)math.utexas.edu). Thanks. Alan Reid Chairman Dept. of Mathematics UT Austin

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Research postdoctoral position in Analysis/Convex Geometry at Kent State
by Dale Alspach 11 Jan '13

11 Jan '13

Kent State University's Department of Mathematical Sciences invites applications for a postdoctoral position in Analysis/Convex Geometry.The appointment will begin August 18, 2013 and is for two academic years with a possible extension for a third year subject to availability of funding. All candidates are required to have a Ph.D. in Mathematics, or equivalent, or to expect to have received such degree by August 2013. The position is intended for new or recent Ph.D. students who have strong research potential.Responsibilities will include participating in joint research projects with the existing faculty. Kent State University is a spacious, residential campus serving more than 42,000 students.It is situated in a small university town within 30 miles of the major metropolitan area of Cleveland, Ohio.The Department of Mathematical Sciences is in the College of Arts and Sciences and offers courses and programs through the doctoral level in applied mathematics, pure mathematics and statistics.For further information about the department, please visit the web site http://www.math.kent.edu. To apply for this position, candidates must first visit the Kent State jobsite at https://jobs.kent.edu to complete an Application and an Academic Data Form. All other documents should be submitted electronically through mathjobs.org <http://mathjobs.org>. If electronic submission is not feasible, submission can be mailed to: Postdoc Search Committee Department of Mathematical Sciences Kent State University Kent, OH 44242-0001. The full application should consist of an AMS coversheet (available through the American Mathematical Society at http://www.ams.org/profession/employment-services/coversheet/coversheet), a cover letter, a curriculum vitae, a publication list, a research statement, and at least three letters of reference. Questions regarding this position may be sent to postdoc-search(a)math.kent.edu <mailto:postdoc-search@math.kent.edu>.Screening of applicants will begin immediately and will continue until the position is filled. Kent State University is an Equal Opportunity, Affirmative Action Employer.

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Ted Odell
by Dale Alspach 09 Jan '13

09 Jan '13

I just learned that Edward (Ted) Odell had a heart attack and died today. Dale Alspach

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Abstract of a paper by Vladimir G. Troitsky and Omid Zabeti
by alspach＠math.okstate.edu 07 Jan '13

07 Jan '13

This is an announcement for the paper "Fremlin tensor products of concavifications of Banach lattices" by Vladimir G. Troitsky and Omid Zabeti. Abstract: Suppose that $E$ is a uniformly complete vector lattice and $p_1, \ldots , p_n$ are positive reals. We prove that the diagonal of the Fremlin projective tensor product of $E_(p_1), \ldots ,E_(p_n)$ can be identified with $E_(p)$ where $p = p_1+\ldots+p_n$ and $E_(p)$ stands for the $p$-concavification of $E$. We also provide a variant of this result for Banach lattices. This extends the main result of [BBPTT]. Archive classification: math.FA Mathematics Subject Classification: Primary: 46B42. Secondary: 46M05, 46B40, 46B45 Remarks: 10 pages Submitted from: ozabeti(a)yahoo.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.0749 or http://arXiv.org/abs/1301.0749

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