Matrix Transformations Between Sets of the Form W- and Operator Generators of Analytic Semigroups

Abstract

In this paper we establish a relation between the notion of operators of analytic semigroups and matrix transformations from a set of sequences into w_∞. We get extensions of some results given by Labbas and de Malafosse concerning applications of the sum of operators in the nondifferential case.

Key words and phrases. Strongly bounded sequences, BK space, generators of analytic semigroup, Banach algebra, bounded operator.

1991 Mathematics Subject Classification. Primary: 35A35, Secondary 40C05, 46A45