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June 2010

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Abstract of a paper by Manuel De la Rosa, Leonhard Frerick, Sophie Grivaux, and Alfredo Peris
by alspach＠fourier.math.okstate.edu 03 Jun '10

03 Jun '10

This is an announcement for the paper "Frequent hypercyclicity, chaos, and unconditional Schauder decompositions" by Manuel De la Rosa, Leonhard Frerick, Sophie Grivaux, and Alfredo Peris. Abstract: We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. This result is extended to complex Frechet spaces with a continuous norm and an unconditional Schauder decomposition, and also to complex Frechet spaces with an unconditional basis, which gives a partial positive answer to a problem posed by Bonet. We also solve a problem of Bes and Chan in the negative by presenting hypercyclic, but non-chaotic operators on \C^\N. We extend the main result to C_0-semigroups of operators. Finally, in contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator. Archive classification: math.FA Submitted from: grivaux(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.1416 or http://arXiv.org/abs/1005.1416

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Abstract of a paper by Daniel A. Klain
by alspach＠fourier.math.okstate.edu 03 Jun '10

03 Jun '10

This is an announcement for the paper "On the equality conditions of the Brunn-Minkowski theorem" by Daniel A. Klain. Abstract: This article describes a new proof of the equality condition for the Brunn-Minkowski inequality. Archive classification: math.MG math.CA math.FA Mathematics Subject Classification: 52A20, 52A38, 52A39, 52A40 Remarks: 9 pages Submitted from: daniel_klain(a)uml.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.1409 or http://arXiv.org/abs/1005.1409

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