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The Induced Semigroup of Schwarz Maps to the Space of Hilbert-Schmidt Operators
Journal article   Open access   Peer reviewed

The Induced Semigroup of Schwarz Maps to the Space of Hilbert-Schmidt Operators

George Androulakis, Alexander Wiedemann and Matthew Ziemke
Mathematical physics, analysis, and geometry, v 23(1)
03 Mar 2020
DOI: https://doi.org/10.1007/s11040-020-09334-6
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
http://arxiv.org/abs/1906.05905View
SubmittedOpen Access (License Unspecified),  Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Physics Physics, Mathematical Science & Technology
We prove that for every semigroup of Schwarz maps on the von Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space of Hilbert-Schmidt operators of the Hilbert space. Moreover, we show that if the original semigroup is weak* continuous then the associated semigroup is strongly continuous. We introduce the notion of the extended generator of a semigroup on the bounded operators of a Hilbert space with respect to an orthonormal basis of the Hilbert space. We describe the form of the generator of a quantum Markov semigroup on the von Neumann algebra of all bounded linear operators on a Hilbert space which has an invariant faithful normal state under the assumption that the generator of the associated semigroup has compact resolvent.

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Collaboration types
Domestic collaboration
Web of Science research areas
Mathematics, Applied
Physics, Mathematical
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