Regularities in noncommutative Banach algebras

Dosiev A.

INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.61, no.3, pp.341-364, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 3
  • Publication Date: 2008
  • Doi Number: 10.1007/s00020-008-1593-6
  • Journal Name: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.341-364
  • Keywords: regularities, subspectrum, characters, JOINT SPECTRA, SUBALGEBRAS, PROPERTY, FAMILY

Abstract

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.