Vol. 19, No. 1, 1966

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Contraction semi-groups in a function space

James Robert Dorroh

Vol. 19 (1966), No. 1, 35–38

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
Received: 19 October 1965
Revised: 2 December 1965
Published: 1 October 1966
James Robert Dorroh