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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-3,
author = {Derek Kitson},
title = {Ascent and descent for sets of operators},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {151-161},
zbl = {1170.47003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-3}
}
Derek Kitson. Ascent and descent for sets of operators. Studia Mathematica, Tome 192 (2009) pp. 151-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-3/