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Ascent and descent for sets of operators

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<mark>Journal publication date</mark>2009
<mark>Journal</mark>Studia Mathematica
Issue number2
Number of pages11
Pages (from-to)151-161
Publication StatusPublished
<mark>Original language</mark>English


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.