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Local operator multipliers and positivity

N. M. Steen ; I. G. Todorov ; Lyudmila Turowska (Institutionen för matematiska vetenskaper, matematik)
Journal of Functional Analysis (0022-1236). Vol. 267 (2014), 1, p. 80-111.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Positive, Local, Schur multiplier, Operator multiplier


Preprint available at: http://arxiv.org/abs/1206.3889v1



Denna post skapades 2014-06-26. Senast ändrad 2016-06-30.
CPL Pubid: 199689

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur