Banach April 2009

banach@mathdept.okstate.edu

2 participants
3 discussions

NBFAS + Graham Jameson Meeting 25-26 May 2009
by Niels Jakob Laustsen 23 Apr '09

23 Apr '09

The Department of Mathematics and Statistics at Lancaster University, UK, will host two meetings with a common theme of Banach spaces on 25-26 May 2009. The first, starting after lunch on Monday 25th May, is a meeting of the North British Functional Analysis Seminar (NBFAS); the NBFAS speaker is Stephen J. Dilworth (South Carolina, USA). The second meeting, on Tuesday 26th May, is in honour of GrahamJameson on the occasion of his retirement, celebrating his many significant contributions to the department and the wider mathematical community during his 35-year career in Lancaster. There will be six invited one-hour talks given by the following speakers: - Timothy Feeman (Villanova, USA), - Richard Haydon (Oxford, UK), - Rafal Latala (Warsaw, Poland), - Edward W. Odell, (Texas, USA), - Charles J. Read (Leeds, UK), and - Thomas Schlumprecht (Texas A&M, USA). This meeting is supported by a London Mathematical Society Scheme 1 conference grant. There is support available for UK graduate students; the deadline for applications for such support is 1st May. Full details of both meetings (including registration, schedule, travel and accommodation) can be found at http://www.maths.lancs.ac.uk/jameson For more information, please contact the organizer Niels J. Laustsen (email: n.laustsen(a)lancaster.ac.uk).

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Abstract of a paper by Daniel Freeman, Edward Odell, and Thomas Schlumprecht
by alspach＠fourier.math.okstate.edu 07 Apr '09

07 Apr '09

This is an announcement for the paper "The universality of $\ell_1$ as a dual space" by Daniel Freeman, Edward Odell, and Thomas Schlumprecht. Abstract: Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\L_\infty$ space $Z$ whose dual is isomorphic to $\ell_1$. If $X$ has a shrinking finite dimensional decomposition and $X^*$ does not contain an isomorph of $\ell_1$, then we construct such a $Z$, as above, not containing an isomorph of $c_0$.If $X$ is separable and reflexive, we show that $Z$ can be made to be somewhat reflexive. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 33 pages The source file(s), fos3.tex: 130106 bytes, is(are) stored in gzipped form as 0904.0462.gz with size 37kb. The corresponding postcript file has gzipped size 218kb. Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.0462 or http://arXiv.org/abs/0904.0462 or by email in unzipped form by transmitting an empty message with subject line uget 0904.0462 or in gzipped form by using subject line get 0904.0462 to: math(a)arXiv.org.

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Abstract of a paper by Joel H. Shapiro
by alspach＠fourier.math.okstate.edu 07 Apr '09

07 Apr '09

This is an announcement for the paper "Eigenfunctions for hyperbolic rcmposition roerators---redux" by Joel H. Shapiro. Abstract: The Invariant Subspace Problem (``ISP'') for Hilbert space operators is known to be equivalent to a question that, on its surface, seems surprisingly concrete: For composition operators induced on the Hardy space H^2 by hyperbolic automorphisms of the unit disc, is every nontrivial minimal invariant subspace one dimensional (i.e., spanned by an eigenvector)? In the hope of reviving interest in the contribution this remarkable result might offer to the studies of both composition operators and the ISP, I revisit some known results, weaken their hypotheses and simplify their proofs. Sample results: If f is a hyperbolic disc automorphism with fixed points at a and b (both necessarily on the unit circle), and C_f the composition operator it induces on H^2, then for every function g in the subspace [{(z-a)(z-a)]^(1/2)H^2, the doubly C_f-cyclic subspace generated by g contains many independent eigenvectors; more precisely, the point spectrum of C_f's restriction to that subspace intersects the unit circle in a set of positive measure. Moreover, this restriction of C_f is hypercyclic (some forward orbit is dense). Archive classification: math.FA math.CV Mathematics Subject Classification: 47B33; 47A15 Remarks: 14 pages The source file(s), shapiro_eigenfns_rvsd.tex: 50277 bytes, is(are) stored in gzipped form as 0904.0022.gz with size 15kb. The corresponding postcript file has gzipped size 98kb. Submitted from: joels314(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.0022 or http://arXiv.org/abs/0904.0022 or by email in unzipped form by transmitting an empty message with subject line uget 0904.0022 or in gzipped form by using subject line get 0904.0022 to: math(a)arXiv.org.

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Banach April 2009