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Regularities in noncommutative Banach algebras

Dosiev, Anar
In this paper we introduce regularities and subspectra in a unital noncommutative Banach algebra and prove that there is a correspondence between them similar to the commutative case. This correspondence involves a radical on a class of Banach algebras equipped with a subspectrum. Taylor and Slodkowski spectra for noncommutative tuples of bounded linear operators are the main examples of subspectra in the noncommutative case.