The quasi-linearity problem for C^∗-algebras

L. J. Bunce and John David Maitland Wright

Vol. 172 (1996), No. 1, 41–47

DOI: 10.2140/pjm.1996.172.41

Abstract

Let 𝒜 be a C^∗-algebra with no quotient isomorphic to the algebra of all two-by-two matrices. Let μ be a quasi-linear functional on 𝒜. Then μ is linear if, and only if, the restriction of μ to the closed unit ball of 𝒜 is uniformly weakly continuous.

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 25 June 1993

Published: 1 January 1996