Event Details

Speaker: Henrik Wirzenius (Czech Academy of Sciences) Title: Closed subideals of operators on Banach spaces

Abstract: I will describe recent joint work with Hans-Olav Tylli (University of Helsinki) on the structure of closed subideals of the Banach algebra L(X) of all bounded linear operators on a Banach space X. A closed subalgebra J⊂L(X) is called a closed subideal of L(X) if there is a closed ideal I of L(X) such that J is a closed ideal of I.

I will also discuss a graded extension of this concept. For n≥2, a closed subalgebra J⊂L(X) is called a closed n-subideal of L(X) if there are closed subalgebras J₀,...,Jₙ of L(X) such that J=Jₙ⊂...⊂J₀=L(X) and each Jₖ is a closed ideal of J_{k-1}. In particular, I will present examples of Banach spaces X for which L(X) contains closed n-subideals that are not closed (n-1)-subideals.