On stability of -semigroups

Author:
Vu Quoc Phong

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2871-2879

MSC (2000):
Primary 47D06

DOI:
https://doi.org/10.1090/S0002-9939-01-05614-3

Published electronically:
May 10, 2001

MathSciNet review:
1707013

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We prove that if is a -semigroup on a Hilbert space , then (a) if and only if , for all , and (b) is exponentially stable if and only if , for all . Analogous, but weaker, statements also hold for semigroups on Banach spaces.

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Additional Information

**Vu Quoc Phong**

Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701

Email:
qvu@oucsace.cs.ohiou.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-05614-3

Received by editor(s):
February 20, 1998

Received by editor(s) in revised form:
May 26, 1999

Published electronically:
May 10, 2001

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society