The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.
@article{bwmeta1.element.bwnjournal-article-smv115i1p87bwm,
author = {Bruce Barnes},
title = {Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {87-103},
zbl = {0831.46049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv115i1p87bwm}
}
Barnes, Bruce. Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras. Studia Mathematica, Tome 113 (1995) pp. 87-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv115i1p87bwm/
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