October 2012 - 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 J. Lopez-Abad
by alspach＠math.okstate.edu 26 Oct '12

26 Oct '12

This is an announcement for the paper "A Bourgain-Pisier construction for general Banach spaces" by J. Lopez-Abad. Abstract: We prove that every Banach space, not necessarily separable, can be isometrically embedded into a $\mathcal L_{\infty}$-space in a way that the corresponding quotient has the Radon-Nikodym and the Schur properties. As a consequence, we obtain $\mathcal L_\infty$ spaces of arbitrary large densities with the Schur and the Radon-Nikodym properties. This extents the a classical result by J. Bourgain and G. Pisier. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B26 Submitted from: abad(a)icmat.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.5728 or http://arXiv.org/abs/1210.5728

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Abstract of a paper by Rafa Espinola and Miguel Lacruz
by alspach＠math.okstate.edu 26 Oct '12

26 Oct '12

This is an announcement for the paper "Applications of fixed point theorems in the theory of invariant subspaces" by Rafa Espinola and Miguel Lacruz. Abstract: We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach space. Archive classification: math.OA Mathematics Subject Classification: 47A15, 47H10 Remarks: 13 pages, to appear in Fixed Point Theory and Applications Submitted from: lacruz(a)us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.5557 or http://arXiv.org/abs/1210.5557

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Abstract of a paper by Ludek Zajicek
by alspach＠math.okstate.edu 26 Oct '12

26 Oct '12

This is an announcement for the paper "Hadamard differentiability via Gateaux differentiability" by Ludek Zajicek. Abstract: Let $X$ be a separable Banach space, $Y$ a Banach space and $f: X \to Y$ a mapping. We prove that there exists a $\sigma$-directionally porous set $A\subset X$ such that if $x\in X \setminus A$, $f$ is Lipschitz at $x$, and $f$ is G\^ateaux differentiable at $x$, then $f$ is Hadamard differentiable at $x$. If $f$ is Borel measurable (or has the Baire property) and is G\^ ateaux differentiable at all points, then $f$ is Hadamard differentiable at all points except a set which is $\sigma$-directionally porous set (and so is Aronszajn null, Haar null and $\Gamma$-null). Consequently, an everywhere G\^ ateaux differentiable $f: \R^n \to Y$ is Fr\' echet differentiable except a nowhere dense $\sigma$-porous set. Archive classification: math.FA Mathematics Subject Classification: Primary: 46G05, Secondary: 26B05, 49J50 Remarks: 9 pages Submitted from: zajicek(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.4715 or http://arXiv.org/abs/1210.4715

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Abstract of a paper by Vitali Milman and Liran Rotem
by alspach＠math.okstate.edu 26 Oct '12

26 Oct '12

This is an announcement for the paper "Mixed integrals and related inequalities" by Vitali Milman and Liran Rotem. Abstract: In this paper we define an addition operation on the class of quasi-concave functions. While the new operation is similar to the well-known sup-convolution, it has the property that it polarizes the Lebesgue integral. This allows us to define mixed integrals, which are the functional analogs of the classic mixed volumes. We extend various classic inequalities, such as the Brunn-Minkowski and the Alexandrov-Fenchel inequality, to the functional setting. For general quasi-concave functions, this is done by restating those results in the language of rearrangement inequalities. Restricting ourselves to log-concave functions, we prove generalizations of the Alexandrov inequalities in a more familiar form. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A39, 26B25 Remarks: 30 pages Submitted from: liranro1(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.4346 or http://arXiv.org/abs/1210.4346

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Abstract of a paper by Stephan Fackler
by alspach＠math.okstate.edu 26 Oct '12

26 Oct '12

This is an announcement for the paper "The Kalton-Lancien theorem revisited: Maximal regularity does not extrapolate" by Stephan Fackler. Abstract: We give a new more explicit proof of a result by Kalton & Lancien stating that on each Banach space with an unconditional basis not isomorphic to a Hilbert space there exists a generator of a holomorphic semigroup which does not have maximal regularity. In particular, we show that there always exists a Schauder basis (f_m) such that the generator is a Schauder multiplier associated to the sequence (2^m). Moreover, we show that maximal regularity does not extrapolate: we construct consistent holomorphic semigroups (T_p(t)) on L^p for p in (1, \infty) which have maximal regularity if and only if p = 2. These assertions were both open problems. Our approach is completely different than the one of Kalton & Lancien. We use the characterization of maximal regularity by R-sectoriality for our construction. Archive classification: math.FA math.AP Mathematics Subject Classification: 35K90, 47D06 (Primary) 46B15 (Secondary) Remarks: 16 pages Submitted from: stephan.fackler(a)uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.4333 or http://arXiv.org/abs/1210.4333

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Abstract of a paper by Philip A.H. Brooker
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Szlenk and $w^\ast$-dentability indices of the Banach spaces $C([0,\alpha])$" by Philip A.H. Brooker. Abstract: Let $\alpha$ be an infinite ordinal and $\gamma$ the unique ordinal satisfying $\omega^{\omega^\gamma}\leq \alpha < \omega^{\omega^{\gamma+1}}$. We show that the Banach space $C([0,\,\alpha])$ of all continuous scalar-valued functions on the compact ordinal interval $[0,\,\alpha]$ has Szlenk index equal to $\omega^{\gamma+1}$ and $w^\ast$-dentability index equal to $\omega^{1+\gamma+1}$. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B20 Submitted from: philip.a.h.brooker(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.3696 or http://arXiv.org/abs/1210.3696

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Abstract of a paper by Geraldo Botelho, Daniel Pellegrino, and Pilar Rueda
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "On Pietsch measures for summing operators and dominated polynomials" by Geraldo Botelho, Daniel Pellegrino, and Pilar Rueda. Abstract: We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials. Archive classification: math.FA Mathematics Subject Classification: 28C15, 46G25, 47B10, 47L22 Remarks: 13 pages Submitted from: pilar.rueda(a)uv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.3332 or http://arXiv.org/abs/1210.3332

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Abstract of a paper by S.A. Argyros, A. Manoussakis, and M. Petrakis
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Function spaces not containing $\ell_{1}$" by S.A. Argyros, A. Manoussakis, and M. Petrakis. Abstract: For $\Omega$ bounded and open subset of $\mathbb{R}^{d_{0}}$ and $X$ a reflexive Banach space with $1$-symmetric basis, the function space $JF_{X}(\Omega)$ is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature that $JF_{X}(\Omega)$ does not contain an isomorphic copy of $\ell_{1}$. We also investigate the structure of these spaces and their duals. Archive classification: math.FA Mathematics Subject Classification: 46B10 Citation: Israel Journal of Mathematics 135 (2003), 29-81 Submitted from: amanousakis(a)isc.tuc.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.2379 or http://arXiv.org/abs/1210.2379

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Abstract of a paper by Henning Kempka and Jan Vybiral
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Lorentz spaces with variable exponents" by Henning Kempka and Jan Vybiral. Abstract: We introduce Lorentz spaces $L_{p(\cdot),q}(\R^n)$ and $L_{p(\cdot),q(\cdot)}(\R^n)$ with variable exponents. We prove several basic properties of these spaces including embeddings and the identity $L_{p(\cdot),p(\cdot)}(\R^n)=L_{p(\cdot)}(\R^n)$. We also show that these spaces arise through real interpolation between $L_{\p}(\R^n)$ and $L_\infty(\R^n)$. Furthermore, we answer in a negative way the question posed in \cite{DHN} whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability. Archive classification: math.FA Submitted from: henning.kempka(a)uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.1738 or http://arXiv.org/abs/1210.1738

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