The index of a quantum dynamical semigroup

DOI10.1006/jfan.1996.3045zbMath0923.46065arXivfunct-an/9705005OpenAlexW2073090663MaRDI QIDQ1369781

William Arveson

Publication date: 21 March 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/funct-an/9705005

zbMATH Keywords

covariance functioninner product spacequantum dynamical semigroupminimal dilationCP semigroup of normal completely positive mapsindex of \(E_0\)-semigroupsindex of a unital completely positive semigrouppositive semidefinite sesquilinear form

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55)

Related Items (16)

On the product system of a completely positive semigroup ⋮ QUANTUM MARKOV SEMIGROUPS: PRODUCT SYSTEMS AND SUBORDINATION ⋮ QUANTUM MARKOV PROCESSES (CORRESPONDENCES AND DILATIONS) ⋮ Dequantization via quantum channels ⋮ Invariants for normal completely positive maps on the hyperfinite \(II_1\) factor ⋮ CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond ⋮ \(C^\ast\)-subproduct and product systems ⋮ Classification of 𝐸₀–semigroups by product systems ⋮ Detailed balance as a quantum-group symmetry of Kraus operators ⋮ Constructing proper Markov semigroups for Arveson systems ⋮ ON THE INDEX AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS ⋮ Subsystems of Fock need not be Fock: Spatial CP-semigroups ⋮ On type II\(_{0}\) \(E_{0}\)-semigroups induced by boundary weight doubles ⋮ Subalgebras of \(C^*\)-algebras. III: Multivariable operator theory ⋮ Spatial Markov semigroups admit Hudson-Parthasarathy dilations ⋮ Markovian cocycles on operator algebras adapted to a Fock filtration

Cites Work

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• A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
• An addition formula for the index of semigroups of endomorphisms of B(H)
• Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
• ON THE INDEX AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS
• Continuous analogues of Fock space
• Noncommutative flows I: dynamical invariants
• Minimal E_0-semigroups
• NEW EXAMPLES OF CONTINUOUS SPATIAL SEMIGROUPS OF *-ENDOMORPHISMS OF ${\mathfrak B} ({\mathfrak h})$
• An Index Theory For Quantum Dynamical Semigroups

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