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A CHARACTERIZATION OF STRONGLY CONTINUOUS GROUPS OF LINEAR OPERATORS ON A HILBERT SPACE

Published online by Cambridge University Press:  01 January 2000

KANGSHENG LIU
KANGSHENG LIU
Affiliation:
Department of Applied Mathematics, Zhejiang University, Hangzhou, 310027, China
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Abstract

It is proved that the infinitesimal generator A of a strongly continuous semigroup of linear operators on a Hilbert space also generates a strongly continuous group if and only if the resolvent of −A, (λ+A)−1, is also a bounded function on some right-hand-side half plane of complex numbers, and converges strongly to zero as the real part of λ tends to infinity. An application to a partial differential equation is given.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 1 , January 2000 , pp. 54 - 62
Copyright
© The London Mathematical Society 2000

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