 

Mark Tomforde
Continuity of ring *homomorphisms between C*algebras


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


Abstract
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 772043008, USA
tomforde@math.uh.edu

