Banach

banach@mathdept.okstate.edu

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Abstract of a paper by D. Drivaliaris and N. Yannakakis
by alspach＠fourier.math.okstate.edu 03 Jun '08

03 Jun '08

This is an announcement for the paper "Hilbert space structure and positive operators" by D. Drivaliaris and N. Yannakakis. Abstract: Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially complemented subspace which is isomorphic to a Hilbert space. We also treat the non-symmetric case. Archive classification: math.FA Mathematics Subject Classification: 46B03; 46C15; 47B99 Citation: Journal of Mathematical Analysis and Applications 305 (2) (2005), The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4721 or http://arXiv.org/abs/0805.4721 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4721 or in gzipped form by using subject line get 0805.4721 to: math(a)arXiv.org.

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Abstract of a paper by D. Drivaliaris and N. Yannakakis
by alspach＠fourier.math.okstate.edu 03 Jun '08

03 Jun '08

This is an announcement for the paper "Subspaces with a common complement in a Banach space" by D. Drivaliaris and N. Yannakakis. Abstract: We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution S on X exchanging the two subspaces, such that I+S is bounded from below on their union. Moreover we show that, in a separable Hilbert space, the only pairs of subspaces with a common complement are those which are either equivalently positioned or not completely asymptotic to one another. We also obtain characterizations for the existence of a common complement for subspaces with closed sum. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46C05; 47A05 Citation: Studia Mathematica 182 (2) (2007), 141-164 The source file(s), common_arxiv.tex: 74237 bytes, is(are) stored in gzipped form as 0805.4707.gz with size 16kb. The corresponding postcript file has gzipped size 104kb. Submitted from: d.drivaliaris(a)fme.aegean.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4707 or http://arXiv.org/abs/0805.4707 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4707 or in gzipped form by using subject line get 0805.4707 to: math(a)arXiv.org.

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Abstract of a paper by Craig Calcaterra and Axel Boldt
by alspach＠fourier.math.okstate.edu 29 May '08

29 May '08

This is an announcement for the paper "Approximating with Gaussians" by Craig Calcaterra and Axel Boldt. Abstract: Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares. Taking the Fourier transform of this result shows low-frequency trigonometric series are dense in L^2 with Gaussian weight function. Archive classification: math.CA math.FA Mathematics Subject Classification: 41A30; 42A32; 42C10 Remarks: 16 pages, 23 figures The source file(s), AppGaussArXiv3.tex: 61111 bytes I100.png: 14299 bytes I200.png: 7466 bytes I210.png: 8594 bytes I220.png: 8450 bytes I230.png: 9254 bytes I240.png: 8799 bytes I250.png: 8967 bytes I300.png: 8446 bytes I310.png: 10845 bytes I311.png: 10945 bytes I320.png: 10846 bytes I330.png: 11696 bytes I340.png: 11710 bytes I350.png: 11061 bytes I400.png: 10444 bytes I410.png: 10145 bytes I420.png: 9810 bytes I500.png: 10246 bytes I510.png: 10478 bytes I520.png: 11634 bytes I530.png: 11233 bytes I600.png: 10241 bytes I610.png: 11497 bytes, is(are) stored in gzipped form as 0805.3795.tar.gz with size 202kb. The corresponding postcript file has gzipped size 279kb. Submitted from: axel.boldt(a)metrostate.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3795 or http://arXiv.org/abs/0805.3795 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3795 or in gzipped form by using subject line get 0805.3795 to: math(a)arXiv.org.

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Abstract of a paper by Chao You and Bao Qi Feng
by alspach＠fourier.math.okstate.edu 27 May '08

27 May '08

This is an announcement for the paper "On distribution and almost convergence of bounded sequences" by Chao You and Bao Qi Feng. Abstract: In this paper, we give the concepts of properly distributed and simply distributed sequences, and prove that they are almost convergent. Basing on these, we review the work of Feng and Li [Feng, B. Q. and Li, J. L., Some estimations of Banach limits, J. Math. Anal. Appl. 323(2006) No. 1, 481-496. MR2262220 46B45 (46A45).], which is shown to be a special case of our generalized theory. Archive classification: math.FA math.GM Mathematics Subject Classification: Primary 40G05, 46A35, 54A20; Secondary 11K36 Remarks: 8 pages The source file(s), Ondistributionandalmostconvergenceofboundedsequences.tex: 25039 bytes, is(are) stored in gzipped form as 0805.3950.gz with size 8kb. The corresponding postcript file has gzipped size 68kb. Submitted from: hityou1982(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3950 or http://arXiv.org/abs/0805.3950 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3950 or in gzipped form by using subject line get 0805.3950 to: math(a)arXiv.org.

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Abstract of a paper by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann
by alspach＠fourier.math.okstate.edu 27 May '08

27 May '08

This is an announcement for the paper "On the nontrivial projection problem" by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann. Abstract: The Nontrivial Projection Problem asks whether every finite-dimensional normed space of dimension greater than one admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension greater than one) is approximately affinely equivalent to a direct product of two bodies of non-trivial dimension. We show that this is true "up to a logarithmic factor." Archive classification: math.FA Mathematics Subject Classification: 46B20, secondary 46B07, 52A21 Remarks: 17 pages The source file(s), NPPforArxiv.tex: 46100 bytes, is(are) stored in gzipped form as 0805.3792.gz with size 17kb. The corresponding postcript file has gzipped size 126kb. Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3792 or http://arXiv.org/abs/0805.3792 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3792 or in gzipped form by using subject line get 0805.3792 to: math(a)arXiv.org.

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Abstract of a paper by Fernando Rambla Jarno Talponen
by alspach＠fourier.math.okstate.edu 27 May '08

27 May '08

This is an announcement for the paper "Simultaneous realization of function space structures in transitive Banach spaces" by Fernando Rambla and Jarno Talponen. Abstract: Let L be a locally compact Hausdorff space and m the Lebesgue measure on the unit interval. We will prove the existence of a transitive Banach space X such that C_{0}(L,X) and the Bochner spaces L^{p}(m,X), 1\leq p\leq \infty, are all isometrically isomorphic to X. Also, more general results of this type are presented. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46E40 The source file(s), BCO4.tex: 52768 bytes, is(are) stored in gzipped form as 0805.3616.gz with size 15kb. The corresponding postcript file has gzipped size 96kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3616 or http://arXiv.org/abs/0805.3616 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3616 or in gzipped form by using subject line get 0805.3616 to: math(a)arXiv.org.

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Abstract of a paper by Mark Rudelson and Roman Vershynin
by alspach＠fourier.math.okstate.edu 27 May '08

27 May '08

This is an announcement for the paper "The least singular value of a random square matrix is O(n^{-1/2})" by Mark Rudelson and Roman Vershynin. Abstract: Let A be a matrix whose entries are real i.i.d. centered random variables with unit variance and suitable moment assumptions. Then the smallest singular value of A is of order n^{-1/2} with high probability. The lower estimate of this type was proved recently by the authors; in this note we establish the matching upper estimate. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52 Remarks: 6 pages The source file(s), square-matrices-reverse.tex: 17210 bytes, is(are) stored in gzipped form as 0805.3407.gz with size 6kb. The corresponding postcript file has gzipped size 68kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3407 or http://arXiv.org/abs/0805.3407 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3407 or in gzipped form by using subject line get 0805.3407 to: math(a)arXiv.org.

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Abstract of a paper by Isabelle Chalendar, Emmanuel Fricain, and Dan Timotin
by alspach＠fourier.math.okstate.edu 27 May '08

27 May '08

This is an announcement for the paper "A note on James spaces and superstrictly singular operators" by Isabelle Chalendar, Emmanuel Fricain, and Dan Timotin. Abstract: An elementary lemma is used in order to show that the natural inclusion $J_p\to J_q$ of James spaces is superstrictly singular for $p<q$. As a consequence, it is shown that an operator without nontrivial invariant subspaces constructed by Charles Read is superstrictly singular. Archive classification: math.FA The source file(s), James.tex: 20594 bytes, is(are) stored in gzipped form as 0805.3409.gz with size 7kb. The corresponding postcript file has gzipped size 70kb. Submitted from: fricain(a)math.univ-lyon1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3409 or http://arXiv.org/abs/0805.3409 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3409 or in gzipped form by using subject line get 0805.3409 to: math(a)arXiv.org.

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Summer school on "Fourier analytic and probabilistic methods in geometric functional, analysis and convexity" (second announcement)
by Artem Zvavitch 15 May '08

15 May '08

Dear Colleagues, We would like to invite you to participate in the summer school on "Fourier analytic and probabilistic methods in geometric functional analysis and convexity" in August 13-20, 2008. The school is being organized by the NSF funded Focused Research Group collaborative project on the same subject (http://www.math.ucdavis.edu/~geofunction/). It is oriented towards graduate students, postdocs and researchers who wish to get an introduction to the subject. The school will feature several series's of lectures. Confirmed speakers include Alexander Barvinok (University of Michigan), Piotr Indyk (Massachusetts Institute of Technology), Fedor Nazarov (University of Wisconsin-Madison), Krzysztof Oleszkiewicz (University of Warsaw), Gideon Schechtman (Weizmann Institute of Scince), Rolf Schneider (University of Freiburg), Mikhail Sodin (Tel Aviv University), Santosh S. Vempala (Georgia Institute of Technology). The school will be hosted by the Department of Mathematical Sciences at Kent State University in August 13-20, 2008 (Arrival date: August 12/ Departure Date August 21). Kent is located in the suburbs of Cleveland, Ohio, where summers are quite beautiful. For further information and breaking news, please, consult http://www.math.kent.edu/math/FAPR.cfm and e-mail to to Dmitry Ryabogin (ryabogin(a)math.kent.edu) or Artem Zvavitch (zvavitch(a)math.kent.edu). We hope to see you in Kent next August. Best Regards, The organizing committee Alex Koldobsky Mark Rudelson Dmitry Ryabogin Stanislaw Szarek Roman Vershynin Elisabeth Werner Artem Zvavitch

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Abstract of a paper by Pandelis Dodos and Jordi Lopez-Abad
by alspach＠fourier.math.okstate.edu 15 May '08

15 May '08

This is an announcement for the paper "On unconditionally saturated Banach spaces" by Pandelis Dodos and Jordi Lopez-Abad. Abstract: We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set $\aaa$, in the Effros-Borel space of subspaces of $C[0,1]$, of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space $Y$, with a Schauder basis, that contains isomorphic copies of every space $X$ in the class $\aaa$. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B03, 46B07, 46B15 Remarks: 16 pages, no figures. Studia Mathematica (to appear) The source file(s), UnconditionallySaturated-ArXiv.tex: 49281 bytes, is(are) stored in gzipped form as 0805.2046.gz with size 14kb. The corresponding postcript file has gzipped size 102kb. Submitted from: pdodos(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2046 or http://arXiv.org/abs/0805.2046 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2046 or in gzipped form by using subject line get 0805.2046 to: math(a)arXiv.org.

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