CONTINUITY OF HOMOMORPHISMS
AND DERIVATIONS ON NORMED
ALGEBRAS WHICH ARE TENSOR
PRODUCTS OF ALGEBRAS
WITH INVOLUTION

A. RODRÍGUEZ-PALACIOS AND M.V. VELASCO

Abstract:

We prove that, if $A$ is a normed $*$-algebra of the form $B\otimes C$ for some central simple finite-dimensional algebra $B$ with involution different from $\pm I_B$ and some algebra $C$ with involution and a unit, then homomorphisms from $A$ to normed algebras and derivations from $A$ to normed $A$-bimodules are continuous whenever they are continuous on the Hermitian part of $A$. When $A$ is associative, some additional information is given.