Journal article
Spectral conditions for stability of one-parameter semigroups
- Abstract:
- Let {S(t): t≥0} be a C0-semigroup on a Banach space Y with generator B and {T(t): t≥0} be a bounded C0-semigroup on a Banach space X with generator A. Suppose that σ(B) ∩ iR is countable, Pσ(A*) ∩ iR is empty and that there is a bounded linear operator C: Y → X with dense range which intertwines the two semigroups. Then ∥T(t)x∥X → 0 as t → ∞, for each x in X. This generalises results of W. Arendt and the author, Yu. I. Lyubich and Vũ Quôc Phóng, and Falun Huang. © 1996 Academic Press, Inc.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 461.2KB, Terms of use)
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- Publisher copy:
- 10.1006/jdeq.1996.0062
Authors
- Publisher:
- Elsevier
- Journal:
- JOURNAL OF DIFFERENTIAL EQUATIONS More from this journal
- Volume:
- 127
- Issue:
- 1
- Pages:
- 87-96
- Publication date:
- 1996-05-01
- DOI:
- ISSN:
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0022-0396
- Language:
-
English
- Pubs id:
-
25217
- UUID:
-
uuid:94f5737f-e40a-4566-a039-522c2643743f
- Local pid:
-
pubs:25217
- Source identifiers:
-
25217
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 1996
- Notes:
- Copyright 1996 Academic Press. Published by Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
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