Spectral conditions for stability of one-parameter semigroups
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...
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| Format: | Journal article |
| Language: | English |
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Elsevier
1996
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| Summary: | 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. |
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