Kitson, Derek
(2011)
*The Browder spectrum of an elementary operator.*
In:
Elementary operators and their applications.
Operator Theory: Advances and Applications
.
Birkhäuser Verlag, Basel, pp. 17-24.
ISBN 9783034800365

## Abstract

We relate the ascent and descent of n-tuples of multiplication operators Ma,b(u)=aub to that of the coefficient Hilbert space operators a, b. For example, if a=(a1,…,an) and b∗=(b∗1,…,b∗m) have finite non-zero ascent and descent s and t, respectively, then the (n+m) -tuple (La,Rb) of left and right multiplication operators has finite ascent and descent s+t−1. . Using these results we obtain a description of the Browder joint spectrum of (La,Rb) and provide formulae for the Browder spectrum of an elementary operator acting on B(H) or on a norm ideal of B(H).