A state-preserving automorphism of a von Neumann algebra induces a canonical unitary operator on the GNS Hilbert space of the state which fixes the vacuum. This unitary commutes with both the modular operator of the state and its modular conjugation. We prove an extension of this result for state-preserving unital completely positive maps. © 2016.

Kunal Krishna Mukherjee

Department of Mathematics

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IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Journal of Mathematical Analysis and Applications

Analyzing endomorphisms and shift E0-semigroups of free products of von Neumann algebras, we construct uncountably many pairwise cocycle inequivalent E0-semigroups on a large class of free Araki-Woods factors. These E0-semigroups are equimodular but not modularly extendable. We also produce conjugate but not cocycle equivalent E0-semigroups on non-type I factors. © 2017 World Scientific Publishing Company.

International Journal of Mathematics

E0-semigroups of free Araki-Woods factors

This article extends the classical theory of joinings of measurable dynamical systems to the noncommutative setting from several interconnected points of view. Among these is a particularly fruitful identification of joinings with equivariant quantum channels between W∗-dynamical systems that provides noncommutative generalizations of many fundamental results of classical joining theory. We obtain fully general analogues of the main classical disjointness characterizations of ergodicity, primeness and mixing phenomena. © The Author(s) 2017.

International Mathematics Research Notices

On noncommutative joinings

Studia Mathematica

Relative weak mixing of W$^*$-dynamical systems via joinings

Communications in Mathematical Physics

The Haagerup Approximation Property for von Neumann Algebras via Quantum Markov Semigroups and Dirichlet Forms

Relatively independent joinings and subsystems of W*-dynamical systems

Factorization and Dilation Problems for Completely Positive Maps on von Neumann Algebras

The modular symmetry of Markov maps

Journal	Journal of Mathematical Analysis and Applications
Publisher	Academic Press Inc.
ISSN	0022247X
Open Access	Yes