Completely semi-$\varphi$-maps
Operator Algebras
2016-08-02 v1
Abstract
We introduce completely semi--maps on Hilbert -modules as a generalization of -maps. This class of maps provides examples of CP-extendable maps which are not CP-H-extendable, in Skeide-Sumesh's sense. Using the CP-extendability of completely semi--maps, we give a representation theorem, similar to Stinespring's representation theorem, for this class of maps which can be considered as strengthened and generalized form of Asadi's and Bhat-Ramesh-Sumesh's analogues of Stinespring representation theorem for -maps. We also define an order relation on the set of all completely semi--maps and establish a Radon-Nikodym type theorem for this class of maps in terms of their representations.
Keywords
Cite
@article{arxiv.1608.00188,
title = {Completely semi-$\varphi$-maps},
author = {Mohammad B. Asadi and Reza Behmani and Ali R. Medghalchi and Hamed Nikpey},
journal= {arXiv preprint arXiv:1608.00188},
year = {2016}
}