Positive extensions of Schur multipliers

Rupert H. Levene; Ying-Fen Lin; Ivan G. Todorov

doi:10.7900/jot.2016may24.2135

Positive extensions of Schur multipliers

Rupert H. Levene, Ying-Fen Lin, Ivan G. Todorov

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Abstract

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We use these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.

Original language	English
Pages (from-to)	45-69
Number of pages	25
Journal	Journal of Operator Theory
Volume	78
Issue number	1
DOIs	https://doi.org/10.7900/jot.2016may24.2135
Publication status	Published - 01 Jul 2017

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Positive extensions of Schur multipliers
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Ying-Fen Lin
- y.linqub.acuk
- School of Mathematics and Physics - Senior Lecturer
- Mathematical Sciences Research Centre
Person: Academic

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title = "Positive extensions of Schur multipliers",

abstract = "We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We use these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.",

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AU - Todorov, Ivan G.

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N2 - We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We use these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.

AB - We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We use these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.

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DO - 10.7900/jot.2016may24.2135

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JO - Journal of Operator Theory

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Positive extensions of Schur multipliers

Abstract

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Ying-Fen Lin

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