QUANTUM MARKOV SEMIGROUPS: PRODUCT SYSTEMS AND SUBORDINATION

DOI10.1142/S0129167X07004254zbMath1125.46057arXivmath/0510653MaRDI QIDQ5297762

Baruch Solel, Paul S. Muhly

Publication date: 13 July 2007

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510653

zbMATH Keywords

completely positive mapproduct systemquantum Markov semigroupcorrespondenceBorel structure\(E_{0}\)-semigroupcocycle of a product system

Mathematics Subject Classification ID

Operator spaces and completely bounded maps (46L07) Quantum stochastic calculus (81S25) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

Related Items (6)

Matricial function theory and weighted shifts ⋮ CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond ⋮ Classification of 𝐸₀–semigroups by product systems ⋮ Structure of block quantum dynamical semigroups and their product systems ⋮ Dilation theory: a guided tour ⋮ Representations of product systems over semigroups and dilations of commuting CP maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete product systems of Hilbert bimodules.
• \(W^ *\)-categories
• The correspondence associated to an inner completely positive map
• Stable isomorphism and strong Morita equivalence of \(C^*\)-algebras
• Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
• Toeplitz algebras associated with endomorphisms and Pimsner-Voiculescu exact sequences
• The index of a quantum dynamical semigroup
• Induced representations of C\(^*\)-algebras
• On the product system of a completely positive semigroup
• Type I product systems of Hilbert modules
• The Borel space of von Neumann algebras on a separable Hilbert space
• Subalgebras of \(C^ *\)-algebras
• Cocycles of CCR flows
• Continuous analogues of Fock space
• An Index Theory for Semigroups of *-Endomorphisms of and Type II₁ Factors.
• On Completely Positive Maps Defined by an Irreducible Correspondence
• The Curvature and Index of Completely Positive Maps
• QUANTUM MARKOV PROCESSES (CORRESPONDENCES AND DILATIONS)
• Minimal isometric dilations of operator cocycles

This page was built for publication: QUANTUM MARKOV SEMIGROUPS: PRODUCT SYSTEMS AND SUBORDINATION