Vol. 41, No. 3, 1972

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Multiplicative perturbation of semigroup generators

Karl Edwin Gustafson and Gunter Lumer

Vol. 41 (1972), No. 3, 731–742

Contraction semigroups of linear operators on a Banach space appear in a wide variety of physical and mathematical situations, and for this reason there has been much interest attached to studying the properties of such semigroups and their infinitesimal generators. In this paper we examine in some detail the question of when one can (left or right) multiply the infinitesimal generator A by another (bounded or unbounded) operator B and still preserve the generator property. Also, we state when polynomials in a generator retain the generator property. Our treatment is not exhaustive but is meant to be representative of the type of results which may be obtained.

Mathematical Subject Classification 2000
Primary: 47D05
Secondary: 47A55, 47B44
Received: 16 March 1970
Revised: 23 June 1971
Published: 1 June 1972
Karl Edwin Gustafson
Gunter Lumer