Tensor product semi-groups

Abstract

Let X and Y be Banach spaces and L(X, Y ) be the space of all bounded linear operators from X to Y .If X = Y we write L(X) forL(X, Y ). Let $X bigotimes Y$ be the tensor product of X and Y , and $X stackrel{a}{bigotimes} Y$ be the completion of $X bigotimes Y$ with respect to a uniform cross norm $alpha$ . In this paper, we present an extension of the Hille-Yosida Theorem to tensor product semigroups. 2000 Mathematics Subject Classifications: Primary 47D03 , Secondary 47D99