SIMULTANEOUS TRIANGULARIZATION IN THE SETTING OF BANACH AND HILBERT SPACES – A SHORT SURVEY

Let X be an arbitrary Banach space. A collection F of bounded operators on X is called simultaneously triangularizable or simply triangularizable if there exists a maximal chain of subspaces of X each of which is invariant under the collection F. In this talk, I will touch upon the notion of simultaneous triangularization in both the Banach and Hilbert space settings hereby I will attempt to present a short survey of the subject.

Keywords:

Banach space , Hilbert space , bounded linear operator , compact linear operator , Cp class operator , triangularizability , complexification of real Banach (resp. Hilbert) spaces , trace , semigroup , algebra