On similarity of nests in hilbert space and in Banach spaces

Abstract

These notes are intended to be expository. We will give an account of much of the work that has been done to date on similarity theory for nest algebras of operators acting on Hilbert space, on some related results for more general reflexive operator algebras, and on some similarity results for nest algebras in the classical Banach spaces. For perspective, we will give definitions and discuss concepts in an abstract Banach space setting whenever possible, and then restrict to special cases (mainly Hilbert spaces) for exposition of concrete results.