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Stability of C0-semigroups and geometry of Banach spaces

Published online by Cambridge University Press:  24 October 2003

RALPH CHILL  and
YURI TOMILOV
RALPH CHILL
Affiliation:
Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany. e-mail: chill@mathematik.uni-ulm.de
YURI TOMILOV
Affiliation:
Faculty of Mathematics and Computer Science, Nicolas Copernicus University, ul. Chopina 12/18, 87-100 Torun, Poland. e-mail: tomilov@mat.uni.torun.pl
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Abstract

We obtain new stability conditions for $C_0$-semigroups on Banach spaces having nontrivial Fourier type. On Hilbert spaces these conditions are sharp. For $C_0$-semigroups on general Banach spaces, we prove a new individual stability criterion. We also show that stronger versions of the range stability condition from [4] are not necessary for stability. This answers an open problem from [4].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 3 , November 2003 , pp. 493 - 511
Copyright
© 2003 Cambridge Philosophical Society

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