Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Ascent and descent for sets of operators
AU - Kitson, Derek
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
U2 - 10.4064/sm191-2-3
DO - 10.4064/sm191-2-3
M3 - Journal article
VL - 191
SP - 151
EP - 161
JO - Studia Mathematica
JF - Studia Mathematica
SN - 0039-3223
IS - 2
ER -