Commutativity Conditions in Algebras with $C^{\ast }$-equalities

M. Oudadess

Abstract


Departing from Fuglede-Putnam-Rosenblum's theorem, we examine several commutativity conditions in involutive algebras with $C^{\ast }$-equalities. Among questions considered are Ogasawara's theorem on operator algebras and Radjavi-Rosenthal's result on an algebra of normal operators. In the frame of $C^{\ast }$-algebras, conditions of apparently different natures turn out to be equivalent. Also, remarks are made about Hirshfeld-Zelazko's problem.

Keywords


Commutativity conditions; $C^{\ast }$-equality; Fuglede-Putnam-Rosenblum; Radjavi-Rosenthal; Ogasawara; Hirshfeld-Zelazko

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DOI: http://dx.doi.org/10.26713%2Fcma.v3i1.145

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