Constructing extensions of CP-maps via tensor dilations with rhe help of von Neumann modules

Rolf Gohm, Michael Skeide

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)

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.
Original languageEnglish
Pages (from-to)291-305
Number of pages15
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume8
Issue number2
DOIs
Publication statusPublished - 02 Jun 2005

Keywords

  • completely positive
  • tensor dilation
  • extension
  • duality
  • von Neumann module

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