TOW-PARAMETER C-SEMIGROUPS AND THE ABSTRACT CAUCHY PROBLEM

Suppose X is a Banach space C is an injective operator in B(X), the space of all bounded linear operators on X. In this note two-parameter C-semigroup of operators is introduced and some properties of two-parameter C-semigroups are discussed. As an application we show that the existence and uniqueness of solution of the 2-abstract Cauchy problem is closely related to the two-parameter C-semigroups of operators.

Keywords:

Two- parameter C-semigroups , Generator , Abstract Cauchy problem