Local operator multipliers and positivity
Journal article, 2014

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.



Schur multiplier

Operator multiplier


N. M. Steen

Queen's University Belfast

I. G. Todorov

Queen's University Belfast

Lyudmyla Turowska

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 267 1 80-111

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