@article{049069f30bc048e7935aa8f85316b2b4,
title = "Three Commuting, Unital, Completely Positive Maps that have no Minimal Dilation",
abstract = "In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann algebra.",
keywords = "Semigroups of completely positive map, dilation",
author = "Shalit, {Orr Moshe} and Michael Skeide",
note = "Funding Information: The authors thank the anonymous referee for his remarks. This research was done partially while the second author was visiting the first author at the Department of Pure Mathematics in the University of Waterloo in November 2009, and while the first author was visiting the second one at the Department of Mathematics and Statistics in Queen{\textquoteright}s University (Kingston) in January 2010. The generous and warm hospitality provided by the departments and by the hosts Ken Davidson and Roland Speicher is greatly appreciated. The second author is supported by research funds of the Italian MIUR",
year = "2011",
month = sep,
day = "1",
doi = "10.1007/s00020-011-1863-6",
language = "English",
volume = "71",
pages = "55--63",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkhauser Verlag Basel",
number = "1",
}