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 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 developed by von Neumann, R. Schatten and W.
Calkin. We will relate the behaviour of the -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.