Extensions of isometric dual representations of semigroups
Let T be a dual representation of a suitable subsemigroup S of a locally compact abelian group G by isometrics on a dual Banach space X = (X*)*. It is shown that (X, T) can be extended to a dual representation of G on a dual Banach space Y containing X, and that this extension can be done in a canon...
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| Format: | Journal article |
| Language: | English |
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1996
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| _version_ | 1797056481504264192 |
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| author | Batty, C Greenfield, D |
| author_facet | Batty, C Greenfield, D |
| author_sort | Batty, C |
| collection | OXFORD |
| description | Let T be a dual representation of a suitable subsemigroup S of a locally compact abelian group G by isometrics on a dual Banach space X = (X*)*. It is shown that (X, T) can be extended to a dual representation of G on a dual Banach space Y containing X, and that this extension can be done in a canonical way. In the case of a representation by *-monomorphisms of a von Neumann algebra, the extension is a representation of G by *-automorphisms of a von Neumann algebra. |
| first_indexed | 2024-03-06T19:23:21Z |
| format | Journal article |
| id | oxford-uuid:1ae033a2-31fa-406d-a0b5-5668c53a2179 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:23:21Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:1ae033a2-31fa-406d-a0b5-5668c53a21792022-03-26T10:57:09ZExtensions of isometric dual representations of semigroupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1ae033a2-31fa-406d-a0b5-5668c53a2179EnglishSymplectic Elements at Oxford1996Batty, CGreenfield, DLet T be a dual representation of a suitable subsemigroup S of a locally compact abelian group G by isometrics on a dual Banach space X = (X*)*. It is shown that (X, T) can be extended to a dual representation of G on a dual Banach space Y containing X, and that this extension can be done in a canonical way. In the case of a representation by *-monomorphisms of a von Neumann algebra, the extension is a representation of G by *-automorphisms of a von Neumann algebra. |
| spellingShingle | Batty, C Greenfield, D Extensions of isometric dual representations of semigroups |
| title | Extensions of isometric dual representations of semigroups |
| title_full | Extensions of isometric dual representations of semigroups |
| title_fullStr | Extensions of isometric dual representations of semigroups |
| title_full_unstemmed | Extensions of isometric dual representations of semigroups |
| title_short | Extensions of isometric dual representations of semigroups |
| title_sort | extensions of isometric dual representations of semigroups |
| work_keys_str_mv | AT battyc extensionsofisometricdualrepresentationsofsemigroups AT greenfieldd extensionsofisometricdualrepresentationsofsemigroups |