IUMJ

Title: Normalisers of CSL algebras

Authors: I. G. Todorov

Issue: Volume 53 (2004), Issue 4, 1013-1036

Abstract:

A coordinate description of the normalisers of CSL algebras is provided. It is shown that the linear span of the normalisers of a continuous nest algebra $\mathcal{A}$, which lie in $\mathcal{A}$, is ultraweakly dense in $\mathcal{A}$. It is proved that, within the classes of continuous nest algebras and totally atomic CSL algebras, the normaliser semigroup determines the algebra up to adjoint. A complete description of the relation between two nest algebras with the same normalisers is given.