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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| _version_ | 1826285868457918464 |
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| author | Batty, C |
| author_facet | Batty, C |
| author_sort | Batty, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:35:17Z |
| format | Journal article |
| id | oxford-uuid:94f5737f-e40a-4566-a039-522c2643743f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:35:17Z |
| publishDate | 1996 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:94f5737f-e40a-4566-a039-522c2643743f2022-03-26T23:42:58ZSpectral conditions for stability of one-parameter semigroupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:94f5737f-e40a-4566-a039-522c2643743fEnglishSymplectic Elements at OxfordElsevier1996Batty, CLet {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. |
| spellingShingle | Batty, C Spectral conditions for stability of one-parameter semigroups |
| title | Spectral conditions for stability of one-parameter semigroups |
| title_full | Spectral conditions for stability of one-parameter semigroups |
| title_fullStr | Spectral conditions for stability of one-parameter semigroups |
| title_full_unstemmed | Spectral conditions for stability of one-parameter semigroups |
| title_short | Spectral conditions for stability of one-parameter semigroups |
| title_sort | spectral conditions for stability of one parameter semigroups |
| work_keys_str_mv | AT battyc spectralconditionsforstabilityofoneparametersemigroups |