Contraction semi-groups in a function space

James Robert Dorroh

Vol. 19 (1966), No. 1, 35–38

DOI: 10.2140/pjm.1966.19.35

Abstract

Using the concepts of a semi inner-product and a dissipative operator, it is proven that if X is a complex Banach space (under the supremum norm) of bounded complex valued functions on a set S, p is a bounded positive function on S which is bounded away from zero, pX ⊂ X, and A is the infinitesimal generator of a strongly continuous (class (C₀)) semi-group of contraction operators in X, then pA is also the infinitesimal generator of such a semi-group.

Mathematical Subject Classification

Primary: 47.25

Secondary: 47.50

Milestones

Received: 19 October 1965

Revised: 2 December 1965

Published: 1 October 1966