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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
1996
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| Summary: | 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. |
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