Local operator multipliers and positivity

N. M. Steen, Ivan G. Todorov, L. Turowska

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
243 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)80-111
JournalJournal of Functional Analysis
Volume267
Issue number1
Early online date05 May 2014
DOIs
Publication statusPublished - 01 Jul 2014

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