October 2014 - 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 Jarno Talponen
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Note on order-isomorphic isometric embeddings of some recent function spaces" by Jarno Talponen. Abstract: We investigate certain recently introduced ODE-determined varying exponent $L^p$ spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent $\ell^p$ space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above $L^p$ spaces to an ultrapower of the above varying exponent $\ell^p$ space. Archive classification: math.FA math.CA Mathematics Subject Classification: 46E30, 46B08, 46B04, 46B42, 46B45, 34-XX Submitted from: talponen(a)iki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4961 or http://arXiv.org/abs/1410.4961

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Abstract of a paper by Julio Flores, Jordi Lopez-Abad, and Pedro Tradacete
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Banach lattice versions of strict singularity" by Julio Flores, Jordi Lopez-Abad, and Pedro Tradacete. Abstract: We explore the relation between lattice versions of strict singularity for operators from a Banach lattice to a Banach space. In particular, we study when the class of disjointly strictly singular operators, those not invertible on the span of any disjoint sequence, coincides with that of lattice strictly singular operators, i.e. those not invertible on any (infinite dimensional) sublattice. New results are given which help to clarify the existing relation between these two classes. Archive classification: math.FA Mathematics Subject Classification: 46B42, 47B60 Submitted from: ptradace(a)math.uc3m.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4752 or http://arXiv.org/abs/1410.4752

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Abstract of a paper by Julio Delgado, Michael Ruzhansky and Baoxiang Wang
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Approximation property and nuclearity on mixed-norm $L^p$, modulation and Wiener amalgam spaces" by Julio Delgado, Michael Ruzhansky and Baoxiang Wang. Abstract: In this paper we first prove the metric approximation property for weighted mixed-norm Lebesgue spaces. Then, using Gabor frame representation we show that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck's theory becomes applicable, and we give criteria for nuclearity and r-nuclearity for operators acting on these space as well as derive the corresponding trace formulae. Finally, we apply the notion of nuclearity to functions of the harmonic oscillator on modulation spaces. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary 46B26, 47B38, Secondary 47G10, 47B06, 42B35 Remarks: 20 pages Submitted from: m.ruzhansky(a)imperial.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4687 or http://arXiv.org/abs/1410.4687

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Abstract of a paper by Michael Cwikel and Richard Rochberg
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Nigel Kalton and complex interpolation of compact operators" by Michael Cwikel and Richard Rochberg. Abstract: This is the fourth of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. This time we discuss Nigel's partial solutions (obtained jointly with one of us) of the problem of whether the complex method of interpolation preserves the compactness of operators. This problem is now 51 years old and still lacks a complete solution. We also survey some other partial solutions of this problem, obtained before and after the above mentioned joint work. We plan a technical sequel to this paper, which may contain some small new results and will probably conclude this series devoted to Nigel's research. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70 Remarks: 12 pages Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4527 or http://arXiv.org/abs/1410.4527

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Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Diameter two properties in James spaces" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda. Abstract: We study the diameter two properties in the spaces $JH$, $JT_\infty$ and $JH_\infty$. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two property, and so the dual norm of these spaces is octahedral. Also we find a closed hyperplane $M$ of $JH_\infty$ whose topological dual space enjoys the $w^*$-strong diameter two property and also $M$ and $M^*$ have an octahedral norm. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Remarks: 19 pages Submitted from: glopezp(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4325 or http://arXiv.org/abs/1410.4325

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Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Subspaces of Banach spaces with big slices" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda. Abstract: We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space $X$ to a subspace $Y$ whenever $Y$ is complemented by a norm one projection with finite-dimensional kernel (respectively the quotient $X/Y$ is finite dimensional, $X/Y$ is strongly regular). Also we study the same problem for dual properties of the above ones, as having octahedral, weakly octahedral or 2-rough norm. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Remarks: 12 pages Submitted from: glopezp(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4324 or http://arXiv.org/abs/1410.4324

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Abstract of a paper by Martino Lupini
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Uniqueness, universality, and homogeneity of the noncommutative Gurarij space" by Martino Lupini. Abstract: We realize the noncommutative Gurarij space $\mathbb{NG}$ defined by Oikhberg as the Fra\"{\i}ss\'{e} limit of the class of finite-dimensional $1$-exact operator spaces. As a consequence we deduce that the noncommutative Gurarij space is unique up to completely isometric isomorphism, homogeneous, and universal among separable $1$-exact operator spaces. Moreover we show that $\mathbb{NG}$ is isometrically isomorphic to the Gurarij Banach space. Therefore $\mathbb{NG}$ can be thought as a canonical operator space structure on the Gurarij Banach space. Archive classification: math.FA math.LO Mathematics Subject Classification: 46L07 (Primary) 03C30 (Secondary) Remarks: 24 pages Submitted from: mlupini(a)yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.3345 or http://arXiv.org/abs/1410.3345

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Abstract of a paper by David Alonso-Gutierrez, Bernardo Gonzalez, C. Hugo Jimenez, and Rafael Villa
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Rogers-Shephard inequality for log-concave functions" by David Alonso-Gutierrez, Bernardo Gonzalez, C. Hugo Jimenez, and Rafael Villa. Abstract: In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary 52A20, Secondary 39B62, 46N10 Remarks: 24 pages Submitted from: carloshugo(a)us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.2556 or http://arXiv.org/abs/1410.2556

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Abstract of a paper by Jochen Gl\"uck
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Spectral and asymptotic properties of contractive semigroups on non-Hilbert spaces" by Jochen Gl\"uck. Abstract: We analyse $C_0$-semigroups of contractive operators on real-valued $L^p$-spaces for $p \not= 2$ and on other classes of non-Hilbert spaces. We show that, under some regularity assumptions on the semigroup, the geometry of the unit ball of those spaces forces the semigroup's generator to have only trivial (point) spectrum on the imaginary axis. This has interesting consequences for the asymptotic behaviour as $t \to \infty$. For example, we can show that a contractive and eventually norm continuous $C_0$-semigroup on a real-valued $L^p$-space automatically converges strongly if $p \not\in \{1,2,\infty\}$. Archive classification: math.FA Mathematics Subject Classification: 47D06 Remarks: 26 pages Submitted from: jochen.glueck(a)uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.2502 or http://arXiv.org/abs/1410.2502

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