Seminário Análise Funcional e Aplicações 

19/09/2008, 15:15 — 16:00 — Sala P3.10, Pavilhão de Matemática
Ivan Todorov, QueenŽs University Belfast, United Kingdom

\(s\)-numbers of elementary operators

A well-known theorem of Fong and Sourour states that an elementary operator acting on the space $B(H)$ of all bounded linear operators on a Hilbert space is compact if and only if the symbols of the operator can be chosen to be compact. In this talk we will give quantitative versions of this result using the notions of an \(s\)-number function introduced by A. Pietsch and the theory of ideals of $B(H)$ developed by von Neumann, R. Schatten and W. Calkin. We will relate the behaviour of the $s$-numbers of a given elementary operator to that of its symbols. We will further extend these results to the case of elementary operators acting on general C*-algebras. The talk is based on a joint work with M. Anoussis and V. Felouzis.