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The Browder spectrum of an elementary operator

Research output: Contribution in Book/Report/ProceedingsChapter (peer-reviewed)

Published

Publication date2011
Host publicationElementary operators and their applications : 3rd International Workshop held at Queen's University Belfast, 14-17 April 2009
EditorsRaul Curto, Martin Mathieu
Place of publicationBasel
PublisherBirkhäuser Verlag
Pages17-24
Number of pages8
ISBN (Print)9783034800365
Original languageEnglish

Publication series

NameOperator Theory: Advances and Applications
Volume212

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).