A remark on the minimal dilation of the semigroup generated by a normal UCP-map

Yusuke Sawada

doi:10.36045/bbms/1561687561

Abstract

There are three known ways to construct the minimal dilation of the discrete semigroup generated by a normal unital completely positive map on a von Neumann algebra, which are given by Arveson, Bhat-Skeide and Muhly-Solel. In this paper, we describe the relation between Bhat-Skeide's and Muhly-Solel's constructions, which is different from the one described by Skeide's commutant duality.

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Yusuke Sawada. "A remark on the minimal dilation of the semigroup generated by a normal UCP-map." Bull. Belg. Math. Soc. Simon Stevin 26 (2) 189 - 202, june 2019. https://doi.org/10.36045/bbms/1561687561

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Published: june 2019

First available in Project Euclid: 28 June 2019

zbMATH: 07094824

MathSciNet: MR3975824

Digital Object Identifier: 10.36045/bbms/1561687561

Subjects:

Primary: 45L55

Secondary: 46L08

Keywords: $W^*$-bimodules , completely positive maps , dilations , relative tensor products , von Neumann algebras

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