Compact multiplication operators on nest algebras

TL;DR

This paper characterizes compact and weakly compact multiplication operators on nest algebras, describing the ideal generated by compact elements and showing the absence of non-zero weakly compact operators on a certain quotient.

Contribution

It provides a new characterization of compact and weakly compact multiplication operators on nest algebras and describes the associated closed ideal.

Findings

Characterization of compact multiplication operators on nest algebras

Description of the ideal generated by compact elements

No non-zero weakly compact operators on the quotient AlgN / (AlgN ∩ K(H))

Abstract

Let N be a nest on a Hilbert space H and AlgN the corresponding nest algebra. We obtain a characterization of the compact and weakly compact multiplication operators defined on nest algebras. This characterization leads to a description of the closed ideal generated by the compact elements of AlgN . We also show that there is no non-zero weakly compact multiplication operator on AlgN / (AlgN $\cap$ K(H)).