Geodesic
Axiomatic theory of spectrum III: semiregularities
Studia Mathematica, Tome 142 (2000) no. 2, pp. 159-169

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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). 
Vladimír Müller. Axiomatic theory of spectrum III: semiregularities. Studia Mathematica, Tome 142 (2000) no. 2, pp. 159-169. doi: 10.4064/sm-142-2-159-169
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