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

Yusuke Sawada

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

Yusuke Sawada

Operator Algebras · Submitted 25 May 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we clarify the relation of the constructions by Bhat-Skeide and Muhly-Solel.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

There are known three 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 clarify the relation of the constructions by Bhat-Skeide and Muhly-Solel.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	There are known three 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.	background 1.00	0.03	0.04	asserted 1.00
s1	In this paper, we clarify the relation of the constructions by Bhat-Skeide and Muhly-Solel.	contribution 0.99	0.88	0.30	asserted 0.99

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Original abstract

There are known three 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 clarify the relation of the constructions by Bhat-Skeide and Muhly-Solel.

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Further results and a brief survey over the latest developments can be found in [ref] and [ref] .

Unitary Dilations of Discrete-Time Quantum-Dynamical Semigroups · Introduction · 1.00

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