Constructing Extensions of CP-Maps via Tensor Dilations with the Help of Von Neumann Modules
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 also other dualities, known and new, find their natural common place.
Cite
@article{arxiv.math/0311110,
title = {Constructing Extensions of CP-Maps via Tensor Dilations with the Help of Von Neumann Modules},
author = {Rolf Gohm and Michael Skeide},
journal= {arXiv preprint arXiv:math/0311110},
year = {2007}
}
Comments
To appear in Infinite Dimensional Analysis and Quantum Probability 2005. This version replaces the first one submitted under the titel "Normal CP-Maps admit Weak Tensor Dilations". The old titel was missleading, as it puts accent onto the wrong things. We rewrote the abstract and largely the second half of the introduction. A couple of typos has been eliminated, but for the rest the main body of the paper remained unchanged