On unitary extensions of multiplicative families of partial isometries with a generating subspace (Q2464352)
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| Language | Label | Description | Also known as |
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| English | On unitary extensions of multiplicative families of partial isometries with a generating subspace |
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On unitary extensions of multiplicative families of partial isometries with a generating subspace (English)
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19 December 2007
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The main object under consideration in the present paper is a multiplicative family of operator-valued functions of two variables, the first one varies on a generalized interval of an abelian ordered group, and the second one on an abelian group. Certain generalizations of the classical Krein's extension theorem and the result of Cooper about unitary extensions of one-parameter semigroups of isometries on the real line are obtained. Applications to the problem of extending locally defined positive definite functions are given.
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partial isometries
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ordered groups
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positive definite functions
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unitary representations
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