The quotient algebra of compact-by-approximable operators.

Abstract: Let $K(X)$ denote the Banach algebra of compact operators acting on a Banach space $X$ and $A(X)$ the uniform closure of the bounded finite rank operators. In this talk I will describe joint work with Hans-Olav Tylli (University of Helsinki) on the quotient algebra $K(X)/A(X)$ of compact-by-approximable operators. This is a radical Banach algebra that is poorly understood, mainly because $K(X)/A(X)$ is non-trivial only within the class of Banach spaces $X$ failing the approximation property. I will focus on the size and algebraic structure of $K(X)/A(X)$.

functional analysisgroup theoryoperator algebras

Audience: researchers in the topic

Groups, Operators, and Banach Algebras Webinar

Series comments: This is an online seminar series for early career researchers working in group theory, operator theory/operator algebra, and Banach algebras. To be added to our mailing list and receive links to our meetings please email us at gobaseminar@gmail.com.