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.
|Number of pages||15|
|Journal||Infinite Dimensional Analysis, Quantum Probability and Related Topics|
|Publication status||Published - 02 Jun 2005|
- completely positive
- tensor dilation
- von Neumann module