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Perturbations of dissipative operators with relative bound one


Author: Paul R. Chernoff
Journal: Proc. Amer. Math. Soc. 33 (1972), 72-74
MSC: Primary 47D05; Secondary 47B44
DOI: https://doi.org/10.1090/S0002-9939-1972-0296745-X
MathSciNet review: 0296745
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Abstract: Let A be the generator of a $ ({C_0})$ contraction semigroup on a Banach space. Let B be a dissipative operator with densely defined adjoint. Assume that the inequality $ \left\Vert {Bx} \right\Vert \leqq \left\Vert {Ax} \right\Vert + b\left\Vert x \right\Vert$ holds on the domain of A. Then the closure of $ A + B$ generates a $ ({C_0})$ contraction semigroup.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296745-X
Keywords: Relatively bounded perturbations, dissipative operators, contraction semigroups
Article copyright: © Copyright 1972 American Mathematical Society

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