Ascent and descent for sets of operators

Volume 191 / 2009

Derek Kitson Studia Mathematica 191 (2009), 151-161 MSC: Primary 47A13, 47A46; Secondary 47A05. DOI: 10.4064/sm191-2-3


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.


  • Derek KitsonSchool of Mathematics
    Trinity College
    Dublin 2, Ireland

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