Introduction to the theory of noncommutative integration

DOI10.1007/BF01103856zbMath0616.46058OpenAlexW1989809706MaRDI QIDQ1821316

N. V. Trunov, Anatoly N. Sherstnev

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1007/bf01103856

zbMATH Keywords

noncommutative integrationintegration in JBW-algebrasIntegration in von Neumann algebrasintegration with respect to unbounded measures on the projections

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Nonassociative selfadjoint operator algebras (46L70)

Related Items (7)

\(L_1\)-space for a positive operator affiliated with von Neumann algebra ⋮ Measures on orthoideals and \(L_1\)-spaces associated with positive operators ⋮ Duality of algebras with an involution and generalized shift operators ⋮ Interpolation of positive operators ⋮ Non-commutative Arens algebras and their derivations ⋮ An extension of the Kreĭn-Smulian and Lozanovskii theorems to metrizable spaces with a cone ⋮ DERIVATIONS ON ALGEBRAS OF MEASURABLE OPERATORS

Cites Work

• Duality for crossed products and the structure of von Neumann algebras of type III
• \(L_ p\)-spaces for von Neumann algebra with reference to a faithful normal semifinite weight
• A theorem about states on quantum logics. States on Jordan algebras
• Applications of the complex interpolation method to a von Neumann algebra: non-commutative \(L^ p\)-spaces
• On normed Jordan algebras which are Banach dual spaces
• Operator valued weights in von Neumann algebras. I
• Operator valued weights in von Neumann algebras. II
• On the spatial theory of von Neumann algebras
• Les espaces \(L^ p\) d'une algebre de von Neumann definies par la derivee spatiale
• Non-commutative Lorentz spaces associated with a semi-finite von Neumann algebra and applications
• A theorem about states on quantum logics. II
• Notes on non-commutative integration
• States on von Neumann algebras
• Normal weights on \(W^*\)-algebras
• A Gelfand-Neumark theorem for Jordan algebras
• Positive cones and \(L^p\)-spaces for von Neumann algebras
• Measures on projections and physical states
• Tomita's theory of modular Hilbert algebras and its applications
• Existence and uniqueness of physical ground states
• Conditional expectations in von Neumann algebras
• The Radon-Nikodym theorem for von Neumann algebras
• A non-commutative extension of abstract integration
• The ^* -Algebra of Unbounded Operators
• Semifinite traces on JBW-algebras
• Measures on Projections in W*-algebras of Type II₁
• Finitely Additive Measures on Projections in Finite W^* -Algebras
• Non-commutative L^P-spaces
• Poids et espérances conditionnelles dans les algèbres de von Neumann
• The Radon-Nikodym Theorem for Finite Rings of Operators
• Formes linéaires sur un anneau d'opérateurs
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