Geodesic
Ascent and descent for sets of operators
Derek Kitson 1
1 School of Mathematics Trinity College Dublin 2, Ireland
Studia Mathematica, Tome 191 (2009) no. 2, pp. 151-161 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm191-2-3
Keywords: extend notion ascent descent operator acting vector space sets operators ascent descent set finite equal rise canonical decomposition space algebras operators unions sets closures sets treated application construct browder joint spectrum commuting tuples bounded operators which compact valued has projection property

Derek Kitson  1

1 School of Mathematics Trinity College Dublin 2, Ireland 
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Derek Kitson. Ascent and descent for sets of operators. Studia Mathematica, Tome 191 (2009) no. 2, pp. 151-161. doi: 10.4064/sm191-2-3

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