Conditionally positive-definite functions in quantum probability theory

DOI10.1007/BF01095976zbMath0735.46044OpenAlexW2015647146MaRDI QIDQ1814450

Alexandr S. Holevo

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf01095976

zbMATH Keywords

functional limit theoremsGNS constructioncanonical representation of positive definite functionscontinuous measurements in quantum mechanicsLévy-Khinchin formula in probabilityLindblad characterization of one-parameter completely positive semigroups on C*-algebraspositive definite complex-valued functions on groups

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Free probability and free operator algebras (46L54) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Quantum stochastic calculus (81S25) Applications of functional analysis in quantum physics (46N50) Limit theorems in probability theory (60F99)

Related Items (1)

Elements of stochastic analysis for the case of Grassmann variables. I: Grassmann stochastic integrals and random processes

Cites Work

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• Infinitely Divisible Measurements in Quantum Probability Theory
• Cohomology of Operator Algebras and Quantum Dynamical Semigroups
• An application of extreme point methods to the representation of infinitely divisible distributions

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