Sesión Análisis Funcional y ComplejoOn complex structures and uniqueness of algebra norms in Banach spaces
Wilson Cuéllar
Universidade de São Paulo, Brasil - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
In this talk, we study the quotient algebra \(L(Z_2)/S(Z_2)\), where \(Z_2\) is the Kalton-Peck space and \(S\) denotes the ideal of strictly singular operators. First, we use quantitative notions of singularity to extend results by Ferenczi and Galego (2007) concerning complex structures on a real Banach space and its hyperplanes. We also investigate the extension properties of operators from \(\ell_2\) to \(Z_2\). Finally, we demonstrate that for a certain algebra norm \(\|\cdot\|_S\), the space \(L(Z_2)/S(Z_2)\) is not complete, which relates to a question of Kalton and Swanson (1982).
Trabajo en conjunto con: Valentin Ferenczi (Universidade de São Paulo).