Commutativity properties in Banach ^∗-algebras

Bertram Yood

Vol. 53 (1974), No. 1, 307–317

DOI: 10.2140/pjm.1974.53.307

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 x^∗y = yx^∗ for all x,y in A where XX^∗ = X^∗X 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