∗-actions in A^∗-algebras

Pak-Ken Wong

Vol. 44 (1973), No. 2, 775–779

DOI: 10.2140/pjm.1973.44.775

Abstract

Let U be the open unit disk in the complex plane and f a function defined on U. We show that if A is an infinite dimensional dual B^∗-algebra, then f defines a ∗-action in A if and only if f is continuous at zero and f(0) = 0. We also obtain that if A is commutative, then f defines a continuous action in A if and only if f is continuous on U and f(0) = 0.

Mathematical Subject Classification 2000

Primary: 46K15

Milestones

Received: 29 October 1971

Published: 1 February 1973