Extensions of semigroups of operators
Let T be a representation of an abelian semigroup S on a Banach space X. We identify a necessary and sufficient condition, which we name superexpansiveness, for T to have an extension to a representation U on a Danach space Y containing X such that each U(t) (t ∈ S) has a contractive inverse. Althou...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2001
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| _version_ | 1797053012207730688 |
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| author | Batty, C Yeates, S |
| author_facet | Batty, C Yeates, S |
| author_sort | Batty, C |
| collection | OXFORD |
| description | Let T be a representation of an abelian semigroup S on a Banach space X. We identify a necessary and sufficient condition, which we name superexpansiveness, for T to have an extension to a representation U on a Danach space Y containing X such that each U(t) (t ∈ S) has a contractive inverse. Although there are many such extensions (Y, U) in general, there is a unique one which has a certain universal property. The spectrum of this extension coincides with the unitary part of the spectrum of T, so various results in spectral theory of group representations can be extended to superexpansive representations. |
| first_indexed | 2024-03-06T18:38:23Z |
| format | Journal article |
| id | oxford-uuid:0c12a7e5-ce38-46be-bdd5-719cd95db01c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:38:23Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:0c12a7e5-ce38-46be-bdd5-719cd95db01c2022-03-26T09:32:50ZExtensions of semigroups of operatorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0c12a7e5-ce38-46be-bdd5-719cd95db01cEnglishSymplectic Elements at Oxford2001Batty, CYeates, SLet T be a representation of an abelian semigroup S on a Banach space X. We identify a necessary and sufficient condition, which we name superexpansiveness, for T to have an extension to a representation U on a Danach space Y containing X such that each U(t) (t ∈ S) has a contractive inverse. Although there are many such extensions (Y, U) in general, there is a unique one which has a certain universal property. The spectrum of this extension coincides with the unitary part of the spectrum of T, so various results in spectral theory of group representations can be extended to superexpansive representations. |
| spellingShingle | Batty, C Yeates, S Extensions of semigroups of operators |
| title | Extensions of semigroups of operators |
| title_full | Extensions of semigroups of operators |
| title_fullStr | Extensions of semigroups of operators |
| title_full_unstemmed | Extensions of semigroups of operators |
| title_short | Extensions of semigroups of operators |
| title_sort | extensions of semigroups of operators |
| work_keys_str_mv | AT battyc extensionsofsemigroupsofoperators AT yeatess extensionsofsemigroupsofoperators |