Given regular normed algebra U with the norm k:kU and normed algebra A with the norm k:kA, and given h 2 rðAÞ, we define a new norm k:kR on U h A; the h-Lau product of U and A, which is a generalization of the operator norm on the unitization of a regular normed algebra. We study this norm and compare it with the ‘1-norm and other regular norms on Lau product of normed algebras (Banach algebras) under suitable conditions. Some of our results are generalizations of similar previous results on unitization. If U and A are C-algebras, we show that U h A with the pointwisedefined involution and k:kR is a C-algebra, and in this way we introduce the Lau product of C-algebras.
