Results on twisted sums of Banach and operator spaces

• Autor(a) principal: Corrêa, Willian Hans Goes
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-06042018-142412/
• topic: Complex interpolation; Espaços de operadores; Interpolação complexa; Operator spaces; Somas torcidas; Twisted sums

In this work we study twisted sums induced by complex interpolation, of Banach spaces as well as of operator spaces. In the first part of the thesis we focus on Banach spaces, and clarify how interpolation of families, as of couples, induces an extension of the interpolation space, called the derived space. We study how the types and cotypes of the spaces being interpolated determine the triviality or singularity of the derived space, and we apply the results to the study of submodules of the Schatten classes and in the obtainment of nontrivial twisted sums in which all of the three spaces in the short exact sequence do not have the approximation property. In the second part we develop the theory of twisted sums in the category of operator spaces and present many examples of twisted sums which are completely singular and completely nontrivial. In particular, we solve two versions of Palais\' problem for operator spaces.