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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Stability of semigroups commuting
with a compact operator

Author: Vu Quôc Phóng
Journal: Proc. Amer. Math. Soc. 124 (1996), 3207-3209
MSC (1991): Primary 47D06
MathSciNet review: 1342041
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Abstract: It is proved that if $T(t), S(t)$ are bounded $C_{0}$-semigroups on Banach spaces $X$ and $Y$, resp., and $C:Y\to X$, $K:Y\to Y$ are bounded operators with dense ranges such that $C$ intertwines $T(t)$ with $S(t)$ and $K$ commutes with $S(t)$, then $T(t)$ is strongly stable provided $A$---the generator of $T(t)$---does not have eigenvalue on $i\mathbf {R}$. An analogous result holds for power-bounded operators.

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Vu Quôc Phóng
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701

Received by editor(s): April 17, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society