Banach July 2012

banach@mathdept.okstate.edu

3 participants
26 discussions

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 Heinrich von Weizsacker
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "In which spaces every curve is Lebesgue-Pettis-integrable?" by Heinrich von Weizsacker. Abstract: In a real locally convex Hausdorff space the closed convex hull of every metrizable compact set is compact if (and only if) every continuous curve has a Pettis integral with respect to Lebesgue measure. For such spaces there is a natural concept of Bochner integrals. Archive classification: math.FA Mathematics Subject Classification: 46G10 Submitted from: weizsaecker(a)mathematik.uni-kl.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.6034 or http://arXiv.org/abs/1207.6034

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Abstract of a paper by Tuomas Hytonen and Assaf Naor
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Pisier's inequality revisited" by Tuomas Hytonen and Assaf Naor. Abstract: Given a Banach space $X$, for $n\in \mathbb N$ and $p\in (1,\infty)$ we investigate the smallest constant $\mathfrak P\in (0,\infty)$ for which every $f_1,\ldots,f_n:\{-1,1\}^n\to X$ satisfy \begin{multline*} \int_{\{-1,1\}^n}\Bigg\|\sum_{j=1}^n \partial_jf_j(\varepsilon)\Bigg\|^pd\mu(\varepsilon)\\\le \mathfrak{P}^p\int_{\{-1,1\}^n}\int_{\{-1,1\}^n}\Bigg\|\sum_{j=1}^n \d_j\Delta f_j(\varepsilon)\Bigg\|^pd\mu(\varepsilon) d\mu(\delta), \end{multline*} where $\mu$ is the uniform probability measure on the discrete hypercube $\{-1,1\}^n$ and $\{\partial_j\}_{j=1}^n$ and $\Delta=\sum_{j=1}^n\partial_j$ are the hypercube partial derivatives and the hypercube Laplacian, respectively. Denoting this constant by $\mathfrak{P}_p^n(X)$, we show that $\mathfrak{P}_p^n(X)\le \sum_{k=1}^{n}\frac{1}{k}$ for every Banach space $(X,\|\cdot\|)$. This extends the classical Pisier inequality, which corresponds to the special case $f_j=\Delta^{-1}\partial_j f$ for some $f:\{-1,1\}^n\to X$. We show that $\sup_{n\in \N}\mathfrak{P}_p^n(X)<\infty$ if either the dual $X^*$ is a $\mathrm{UMD}^+$ Banach space, or for some $\theta\in (0,1)$ we have $X=[H,Y]_\theta$, where $H$ is a Hilbert space and $Y$ is an arbitrary Banach space. It follows that $\sup_{n\in \N}\mathfrak{P}_p^n(X)<\infty$ if $X$ is a Banach lattice of finite cotype. 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/1207.5375 or http://arXiv.org/abs/1207.5375

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Abstract of a paper by Boris Rubin
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Weighted norm inequalities for k-plane transforms" by Boris Rubin. Abstract: We obtain sharp inequalities for the k-plane transform, the ``j-plane to k-plane'' transform, and the corresponding dual transforms, acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Some generalizations and open problems are discussed. Archive classification: math.FA Mathematics Subject Classification: 44A12 Remarks: 16 pages Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.5180 or http://arXiv.org/abs/1207.5180

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Abstract of a paper by Boris Rubin
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "On the Funk-Radon-Helgason inversion method in integral geometry" by Boris Rubin. Abstract: The paper deals with totally geodesic Radon transforms on constant curvature spaces. We study applicability of the historically the first Funk-Radon-Helgason method of mean value operators to reconstruction of continuous and $L^p$ functions from their Radon transforms. New inversion formulas involving Erd\'elyi-Kober type fractional integrals are obtained. Particular emphasis is placed on the choice of the differentiation operator in the spirit of the recent Helgason's formula. Archive classification: math.FA Mathematics Subject Classification: 44A12 Remarks: 29 pages Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.5178 or http://arXiv.org/abs/1207.5178

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Abstract of a paper by S. Waleed Noor
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Embeddings of M\"{u}ntz spaces: composition operators" by S. Waleed Noor. Abstract: Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We discuss how properties of the embedding $M_\Lambda^2\subset L^2(\mu)$, where $\mu$ is a finite positive Borel measure on the interval $[0,1]$, have immediate consequences for composition operators on $M^2_\Lambda$. We give criteria for composition operators to be bounded, compact, or to belong to the Schatten--von Neumann ideals. Archive classification: math.FA Mathematics Subject Classification: 46E15, 46E20, 46E35 Citation: Integral Equations Operator Theory, Springer, 2012 Remarks: 15 Pages Submitted from: waleed_math(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4719 or http://arXiv.org/abs/1207.4719

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Abstract of a paper by Manor Mendel and Assaf Naor
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Nonlinear spectral calculus and super-expanders" by Manor Mendel and Assaf Naor. Abstract: Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Ces\`aro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space. Archive classification: math.MG math.CO math.FA Remarks: Some of the results of this paper were announced in arXiv:0910.2041. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4705 or http://arXiv.org/abs/1207.4705

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Abstract of a paper by Diana Ojeda-Aristizabal
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "A norm for Tsirelson's Banach space" by Diana Ojeda-Aristizabal. Abstract: We give an expression for the norm of the space constructed by Tsirelson. The implicit equation satisfied by this norm is dual to the implicit equation for the norm of the dual of Tsirelson space given by Figiel and Johnson. The expression can be modified to give the norm of the dual of any mixed Tsirelson space. In particular, our results can be adapted to give the norm for the dual of Schlumprecht space. Archive classification: math.FA Mathematics Subject Classification: 46B20 Submitted from: dco34(a)cornell.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4504 or http://arXiv.org/abs/1207.4504

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Abstract of a paper by Peer Christian Kunstmann and Alexander Ullmann
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Rs-sectorial operators and generalized Triebel-Lizorkin spaces" by Peer Christian Kunstmann and Alexander Ullmann. Abstract: We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\mathcal{R}_s$-sectorial operators, which in turn is based on the notion of $\mathcal{R}_s$-bounded sets of operators introduced by Lutz Weis, we obtain a neat theory including equivalence of various norms and a precise description of real and complex interpolation spaces. Another main result of this article is that an $\mathcal{R}_s$-sectorial operator always has a bounded $H^\infty$-functional calculus in its associated generalized Triebel-Lizorkin spaces. Archive classification: math.FA Mathematics Subject Classification: 46E30, 47A60, 47B38 (Primary), 42B25 (Secondary) Remarks: 44 pages Submitted from: alexander.ullmann(a)gmx.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4217 or http://arXiv.org/abs/1207.4217

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Abstract of a paper by Michal Kraus
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Coarse and uniform embeddings between Orlicz sequence spaces" by Michal Kraus. Abstract: We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper Matuszewska-Orlicz indices. Archive classification: math.FA Mathematics Subject Classification: 46B80, 46B20 Remarks: 12 pages Submitted from: mkraus(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3967 or http://arXiv.org/abs/1207.3967

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Banach July 2012