We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).
@article{bwmeta1.element.bwnjournal-article-smv142i2p159bwm,
author = {Vladim\'\i r M\"uller},
title = {Axiomatic theory of spectrum III: semiregularities},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {159-169},
zbl = {0977.47006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p159bwm}
}
Müller, Vladimír. Axiomatic theory of spectrum III: semiregularities. Studia Mathematica, Tome 141 (2000) pp. 159-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p159bwm/
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