Extremal marginals of an unbounded local completely positive and local completely contractive map

Abstract

In this paper, we consider the unbounded local completely positive and local completely contractive maps on a maximal tensor product of unital locally $C^{\ast }$-algebras and discuss on extremal points of certain convex subsets in the set of such maps.

KEYWORDS:

• Quantized domain
• local completely positive maps
• local completely contractive maps
• extremal local completely positive maps
• locally $C^{\ast }$-algebras

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47L55
• 46L60
• 47L30
• 47L75

Acknowledgments

The author would like to thank the referee for his/her useful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, project number PN-III-P4-ID-PCE-2020-0458, within PNCDI III.