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

Authors

  • M. Oudadess c/o A. El Kinani Ecole Normale Superieure Avenus Oued Akrach B.P.~10405, Rabat

DOI:

https://doi.org/10.26713/cma.v3i1.145

Keywords:

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

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.

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CITATION

How to Cite

Oudadess, M. (2012). Commutativity Conditions in Algebras with $C^{\ast }$-equalities. Communications in Mathematics and Applications, 3(1), 61–73. https://doi.org/10.26713/cma.v3i1.145

Issue

Vol. 3 No. 1 (2012)

Section

Research Article

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