Covariant GNS Representation for C*-Dynamical Systems
Carlo Pandiscia
TL;DR
This paper extends the covariant GNS representation to C*-dynamical systems with unital completely positive maps, broadening its applicability and connecting it to reversible dilation theory.
Contribution
It generalizes the covariant GNS representation to include systems with unital completely positive dynamics, expanding the theoretical framework.
Findings
Extended covariant GNS representation to new class of dynamical systems
Connected the representation to reversible dilation theory
Provided a comprehensive overview of applications
Abstract
We extend the covariant GNS representation of Niculescu, Str\"oh and Zsid\'o for C*-dynamical systems with time-evolution of the system (dynamics) a homomorphism of C*-algebras, to any dynamical systems, where the dynamics is an unital completely positive map. We give also an overview on its application to the reversible dilation theory as formulated by B. Kummerer.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Quantum chaos and dynamical systems · Markov Chains and Monte Carlo Methods