New York Journal of Mathematics
Volume 15 (2009) 161-167


Mark Tomforde

Continuity of ring *-homomorphisms between C*-algebras

Published: May 5, 2009
Keywords: C*-algebras, rings, homomorphisms, Jordan morphisms
Subject: 46L05, 16W10

The purpose of this note is to prove that if A and B are unital C*-algebras and φ : A → B is a unital *-preserving ring homomorphism, then φ is contractive; i.e., ∥ φ (a) ∥ ≦ ∥ a ∥ for all a ∈ A. (Note that we do not assume φ is linear.) We use this result to deduce a number of corollaries as well as characterize the form of such unital *-preserving ring homomorphisms.

Author information

Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA