April 2011 - 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 Almut Burchard and Marc Fortier
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "Convergence of random polarziations" by Almut Burchard and Marc Fortier. Abstract: We derive conditions under which random sequences of polarizations converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose distributions may be far from uniform. The proof of convergence hinges on an estimate for the expected distance from the limit that also yields a bound on the rate of convergence. In the special case of i.i.d. sequences, we obtain almost sure convergence even for polarizations chosen at random from small sets. The precise characterization of convergent sequences remains an open problem. These statements about polarization allow us to improve the existing convergence results for Steiner symmetrization. In particular, we show that full rotational symmetry can be achieved by alternating Steiner symmetrization along directions that satisfy an explicit non-degeneracy condition. Finally, we construct examples for dense sequences of directions such that the corresponding Steiner symmetrizations do not converge. Archive classification: math.FA math.PR Mathematics Subject Classification: 60D05 (26D15, 28A75, 52A52) Remarks: 30 pages, 6 figures Submitted from: almut(a)math.toronto.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.4103 or http://arXiv.org/abs/1104.4103

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Abstract of a paper by Christian Rosendal
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "$\alpha$-minimal Banach spaces" by Christian Rosendal. Abstract: A Banach space with a Schauder basis is said to be $\alpha$-minimal for some countable ordinal $\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\alpha$. We prove a dichotomy that characterises when a Banach space has an $\alpha$-minimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characteristic subspaces. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B03, 03E15 Submitted from: rosendal(a)math.uic.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.3543 or http://arXiv.org/abs/1104.3543

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Abstract of a paper by Hulya Duru, Arkady Kitover, and Mehmet Orhon
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "Multiplication operators on vector-valued function spaces" by Hulya Duru, Arkady Kitover, and Mehmet Orhon. Abstract: Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is given by multiplication by a function in $L^{\infty}(\mu).$ In the main result of this paper, we show that an operator $T$ on $E(X)$ is a multiplication operator if and only if $T$ commutes with $L^{\infty}(\mu)$ and leaves invariant the cyclic subspaces generated by the constant vector-valued functions in $E(X).$ As a corollary we show that this is equivalent to $T$ satisfying a functional equation considered by Calabuig, Rodr\'{i}guez, S\'{a}nchez-P\'{e}rez in [3]. Archive classification: math.FA Mathematics Subject Classification: 47B38 (Primary) 46G10, 46B42, 46H25 (Secondary) Submitted from: mo(a)unh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.2806 or http://arXiv.org/abs/1104.2806

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Abstract of a paper by S. Lajara, A. Pallares and S. Troyanski
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "Moduli of convexity and smoothness of reflexive subspaces of L^1" by S. Lajara, A. Pallares and S. Troyanski. Abstract: We show that for any probability measure \mu there exists an equivalent norm on the space L^1(\mu) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B10, 46B20, 46B25 Submitted from: apall(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.2802 or http://arXiv.org/abs/1104.2802

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Abstract of a paper by Peter Elbau
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "Sequential lower semi-continuity of non-local functionals" by Peter Elbau. Abstract: We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which depends on the function values at two different points. The characterisation we get is essentially that the density has to be convex in one variable if we integrate over the other one with an arbitrary test function in it. Moreover, we show that this condition is in the case of non-local functionals on real-valued Lebesgue spaces (up to some equivalence in the density) equivalent to the separate convexity of the density. Archive classification: math.FA Mathematics Subject Classification: 49J05, 49J45 Remarks: 23 pages Submitted from: elbau(a)math.ethz.ch The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.2686 or http://arXiv.org/abs/1104.2686

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Abstract of a paper by Denis Potapov, Fedor Sukochev, and Quanhua Xu
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "On the vector-valued Littlewood-Paley-Rubio de Francia inequality" by Denis Potapov, Fedor Sukochev, and Quanhua Xu. Abstract: The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LPR_p, 2 \leq p < \infty. The paper shows that every Banach lattice whose 2-concavification is a UMD Banach lattice has this property. The paper also shows that every space having LPR_q also has LPR_p with q \leq p < \infty. 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/1104.2671 or http://arXiv.org/abs/1104.2671

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Abstract of a paper by Witold Marciszewski and Grzegorz Plebanek
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "On measures on Rosenthal compacta" by Witold Marciszewski and Grzegorz Plebanek. Abstract: We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every Radon measure on an arbitrary Rosenthal compactum is of countable type. Our approach is based on some caliber-type properties of measures, parameterized by separable metrizable spaces. Archive classification: math.FA Mathematics Subject Classification: 28C15, 46A50 (Primary) 28A60, 54C35 (Secondary) Remarks: 14 pages Submitted from: grzes(a)math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.2639 or http://arXiv.org/abs/1104.2639

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Abstract of a paper by Piotr Nayar and Tomasz Tkocz
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "On a Loomnis-Whitney type inequality for permutationally invariant unconditional convex bodies" by Piotr Nayar and Tomasz Tkocz. Abstract: For a permutationally invariant unconditional convex body K in R^n we define a finite sequence (K_j), j = 1, ..., n of projections of the body K to the space spanned by first j vectors of the standard basis of R^n. We prove that the sequence of volumes (|K_1|, ..., |K_n|) is log-concave. Archive classification: math.FA Mathematics Subject Classification: 52A20 (Primary), 52A40 (Secondary) Remarks: 5 pages Submitted from: t.tkocz(a)students.mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.6232 or http://arXiv.org/abs/1103.6232

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Abstract of a paper by Mark Braverman, Konstantin Makarychev, Yury Makarychev, and Assaf Naor
by alspach＠math.okstate.edu 29 Apr '11

29 Apr '11

This is an announcement for the paper "The Grothendieck constant is strictly smaller than Krivine's bound" by Mark Braverman, Konstantin Makarychev, Yury Makarychev, and Assaf Naor. Abstract: We prove that $K_G<\frac{\pi}{2\log\left(1+\sqrt{2}\right)}$, where $K_G$ is the Grothendieck constant. Archive classification: math.FA Submitted from: naor(a)cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1103.6161 or http://arXiv.org/abs/1103.6161

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