Journal of Operator Theory

Volume 78, Issue 1, Summer 2017 pp. 45-69.

Positive extensions of Schur multipliers

Authors: Rupert H. Levene (1), Ying-Fen Lin (2), and Ivan G. Todorov (3)
Author institution: (1) School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland
(2) Pure Mathematics Research Centre, Queen's University Belfast, Belfast BT7 1NN, U.K.
(3) Pure Mathematics Research Centre, Queen's University Belfast, Belfast BT7 1NN, U.K.

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2016may24.2135
Keywords: Schur multipliers, extensions, masa-bimodules, positive definite functions

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