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Master's Dissertation
DOI
10.11606/D.45.2015.tde-26082015-210548
Document
Author
Full name
Veronica Leão Neves
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Lourenco, Mary Lilian (President)
Fávaro, Vinícius Vieira
Villarroel, Humberto Daniel Carrión
Title in Portuguese
Propriedade Dunford-Pettis alternativa
Keywords in Portuguese
C*-álgebras
Operadores compactos
Propriedade Dunford-Pettis
Propriedade Dunford-Pettis alternativa
Abstract in Portuguese
Este trabalho tem como objetivo estudar a propriedade Dunford-Pettis alternativa (propriedade DP1), como introduzida por Freedman, e algumas de suas caracterizações e relações com outras propriedades. Estudamos caracterizações para alguns espaços de operadores com a propriedade DP1, dadas por Acosta e Peralta. Vimos que um subespaço fechado do espaço dos operadores compactos em um espaço de Banach reflexivo com base de Schauder tem a propriedade DP1 se, e somente se, os operadores avaliação são operadores DP1. Estudamos um resultado análogo para espaços de Hilbert. Como consequência desses resultados, vimos uma caracterização de certas subálgebras fechadas da álgebra dos operadores compactos que possuem a propriedade DP1, supondo que os operadores composição à direita e à esquerda são operadores DP1. Finalmente, estudamos a demonstração feita por Bunce e Peralta de que as propriedades Dunford-Pettis e Duford-Pettis alternativa são equivalentes em C*-álgebras.
Title in English
The alternative Dunford-Pettis property
Keywords in English
C*-algebras
Compact operators
The alternative Dunford-Pettis property
The Dunford-Pettis property
Abstract in English
The main purpose of this work is to study the alternative Dunford-Pettis property (DP1 property), as introduced by Freedman, and some characterizations of the DP1 property and relations of this to other properties. We studied a characterization of certain operator subspaces which have the DP1 property, as given by Acosta and Peralta in \cite. We saw that a closed subspace of the compact operators space in a reflexive Banach space with Schauder basis has the DP1 property if, and only if, the evaluation operators are DP1 operators. We studied a similar result for Hilbert spaces. Consequently, we also saw a characterization of certain closed subalgebras of the compact operators algebra, in which the DP1 property is held by assuming that the right and left composition operators are DP1. Finally, we studied the proof given by Bunce and Peralta that the Dunford-Pettis property and the alternative Duford-Pettis property are equivalent for C*-algebras.
 
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Dissertacao_Veronica.pdf (950.90 Kbytes)
Publishing Date
2015-08-31
 
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