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CONSTRUCTING EXTENSIONS OF CP-MAPS VIA TENSOR DILATIONS WITH THE HELP OF VON NEUMANN MODULES

Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Jahnstraße 15a, 17487 Greifswald, Germany

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MICHAEL SKEIDE

Dipartimento S.E.G.e S., Università degli Studi del Molise, Via de Sanctis, 86100 Campobasso, Italy

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https://doi.org/10.1142/S0219025705001986Cited by:1 (Source: Crossref)

Abstract

We apply Hilbert module methods to show that normal completely positive maps admit weak tensor dilations. Appealing to a duality between weak tensor dilations and extensions of CP-maps, we get an existence proof for certain extensions. We point out that this duality is part of a far reaching duality between a von Neumann bimodule and its commutant in which other dualities, known and new, also find their natural common place.

Keywords:

AMSC: 46L57, 46L53, 46L08

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