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Home > Research > Publications & Outputs > Ascent and descent for sets of operators
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Ascent and descent for sets of operators

Research output: Contribution to journalJournal article

Published

Journal publication date2009
JournalStudia Mathematica
Journal number2
Volume191
Number of pages11
Pages151-161
Original languageEnglish

Abstract

We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded operators which is compact-valued and has the projection property.