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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