Perturbations of dissipative operators with relative bound one

Author:

Chernoff Paul R.

Abstract

Let A be the generator of a ( C 0 ) ({C_0}) contraction semigroup on a Banach space. Let B be a dissipative operator with densely defined adjoint. Assume that the inequality B x A x + b x \left \| {Bx} \right \| \leqq \left \| {Ax} \right \| + b\left \| x \right \| holds on the domain of A. Then the closure of A + B A + B generates a ( C 0 ) ({C_0}) contraction semigroup.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference4 articles.

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4. Generalisations of Rellich’s theorem on perturbation of (essentially) selfadjoint operators;Wüst, Rainer;Math. Z.,1971

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