MULTIPLICATIVITY FACTORS FOR P-SEMINORMS

Abstract

Let S be a p-seminorm on an algebra A. In this paper we study multiplicativity and quadrativity factors for S, i.e., constants mu> 0 and lambda> 0 for which S(xy) <=S(x)S(y) and S(x^2) <=lambdaS(x)2 for all x,y in A. We begin with characterizing these factors in terms of the kernel of S and we also show that p-norms on finite dimensional algebras always have multiplicative factors. We then provide under what conditions does S have multiplicative factors if it has quadrative factors. Finally, we show that if A is commutative then quadrativity factors imply multiplicativity factors.