Commutativity Conditions in Algebras with C^* -equalities - Oudadess, M. (Communications in Mathematics and Applications, 2012)
Departing from Fuglede-Putnam-Rosenblum’s theorem, we examine several commutativity conditions in involutive algebras with C^* -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^* -algebras, conditions of apparently different natures turn out to be equivalent. Also, remarks are made about Hirshfeld-Zelazko’s problem.