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Master's Dissertation
DOI
10.11606/D.45.2018.tde-25122017-132925
Document
Author
Full name
Wilson Albeiro Cuellar Carrera
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Ferenczi, Valentin Raphael Henri (President)
Ascui, Jorge Tulio Mujica
Galego, Eloi Medina
Title in Portuguese
Um espaço de Banach não isomorfo ao conjugado complexo
Keywords in Portuguese
Espaços de Banach
Estruturas complexas
Somas torcidas
Abstract in Portuguese
Neste trabalho fazemos um estudo do conceito de soma torcida de F-espaços. Apresentamos algumas propriedades e simplificações na construção de somas torcidas de F-espaços localmente limitados. Em particular, estudamos uma condição suficiente para que uma soma torcida de espaços de Banach seja um espaço de Banach. Finalmente aplicamos esses conceitos para definir o espaço construído por N. J. Kalton, que é um exemplo de um espaço de Banach não isomorfo ao conjugado complexo. Este espaço X de Kalton corresponde a uma soma torcida de espaços de Hilbert, isto é, X possui um subespaço fechado E tal que E e X/E são isomorfos a espaços de Hilbert.
Title in English
A Banach space not isomorphic to its complex conjugate
Keywords in English
Banach spaces
Complex structures
Twisted sums
Abstract in English
In this work we study the concept of twisted sum of F-spaces. We also study some properties and simplifications in the construction of twisted sums of locally bounded F-spaces. In particular, we study a sufficient condition for a twisted sum of Banach spaces to be a Banach space. Finally we apply these concepts to define the space constructed by N. J. Kalton, which is an example of a Banach space not isomorphic to its complex conjugate. The Kalton space X is a twisted sum of Hilbert spaces, i.e. X has a closed subspace E such that E and X/E are isomorphic to Hilbert spaces.
 
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WCuellarCarrera.pdf (722.16 Kbytes)
Publishing Date
2018-02-08
 
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