Seminário Análise Funcional e Aplicações 

16/04/2010, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Janko Bracic, University of Ljubljana, Slovenia

On the reflexivity of the kernel of an elementary operator

The notion of a reflexive linear space of operators is closely related with the invariant subspace problem for complex Banach spaces. There are several generalizations of this notion. One of them is \(k\)-reflexivity, where \(k\) is an arbitrary positive integer. One can show that a linear space of operators is \(k\)-reflexive if and only if it is an intersection of kernels of a set of elementary operators of length at most \(k\). Thus, it is natural to ask when is the kernel of a given elementary operator \(k\)-reflexive. We will present some results related to this question.