Vol. 53, No. 1, 1974

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Commutativity properties in Banach -algebras

Bertram Yood

Vol. 53 (1974), No. 1, 307–317
Abstract

Let A be a Banach -algebra which has a faithful -representation as bounded linear operators on a flilbert space. It follows from Fuglede’s theorem concerning normal operators on a Hilbert space that xy = yx for all x,y in A where XX = XX and xy = yx. Other commutativity properties in suitable Banach -algebras A involving elements not necessarily normal are considered.

Mathematical Subject Classification 2000
Primary: 46K05
Milestones
Received: 12 November 1973
Published: 1 July 1974
Authors
Bertram Yood