The Browder spectrum of an elementary operator

Kitson, Derek (2011) The Browder spectrum of an elementary operator. In: Elementary operators and their applications : 3rd International Workshop held at Queen's University Belfast, 14-17 April 2009. 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).