An unbounded generalization of the Tomita-Takesaki theory

DOI10.2977/prims/1195177629zbMath0624.47044OpenAlexW2149867899MaRDI QIDQ578572

Atsushi Inoue

Publication date: 1986

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195177629

zbMATH Keywords

unitary groupfixed-point algebrabicommutant\(O^ *_ p\)- algebrascyclic and separating vectorgeneralized von Neumann algebraleft von Neumann algebramodular conjugation operatormodular unbounded left Hilbert algebrasright von Neumann algebraunbounded generalization of von Neumann algebrasunbounded left Hilbert algebras

Mathematics Subject Classification ID

Algebras of unbounded operators; partial algebras of operators (47L60) General theory of von Neumann algebras (46L10) Applications of selfadjoint operator algebras to physics (46L60) Automorphisms of selfadjoint operator algebras (46L40) Hilbert algebras (46K15)

Related Items (15)

On KMS states for self-dual CCR algebras and Bogoliubov automorphism groups ⋮ Extension of unbounded left Hilbert algebras to partial *-algebras ⋮ Cyclic generalized vectors for algebras of unbounded operators ⋮ An unbounded generalization of the Tomita-Takesaki theory. II ⋮ Modular structure of algebras of unbounded operators ⋮ Modular systems induced by trace functionals on algebras of unbounded operators ⋮ An unbounded generalization of Tomita's observable algebras ⋮ Standard systems for semifinite O$^{*}$-algebras ⋮ Partial \(\star\)-algebras of closable operators. II: States and representations of partial \(\star\)-algebras ⋮ Representability of invariant positive sesquilinear forms on partial *-algebras ⋮ Unnamed Item ⋮ An unbounded generalization of Hilbert algebras ⋮ Standard generalized vectors and \({}^*\)-automorphism groups of partial \(O^*\)-algebras ⋮ Trace representation of weights on algebras of unbounded operators ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extension of Tomita-Takesaki theory to the unbounded algebra of the canonical commutation relations
• The order structure of topological \(^*\)-algebras of unbounded operators. I
• A class of unbounded operator algebras
• A bounded operator approach to Tomita-Takesaki theory
• Unbounded representations of \(^*\)-algebras
• On trace representation of linear functionals on unbounded operator algebras
• A new approach to the Tomita-Takesaki theory of generalized Hilbert algebras
• Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon-Nikodym theorem with a chain rule
• Positive linear functionals on \(^ *\)-algebras of unbounded operators
• Tomita's theory of modular Hilbert algebras and its applications
• Self-adjoint algebras of unbounded operators
• Topological algebras of operators
• Normal states on algebras of unbounded operators
• A non-commutative extension of abstract integration
• Commutants and bicommutants of algebras of unbounded operators
• V*-algebras: A particular class of unbounded operator algebras
• STANDARD REPRESENTATIONS INDUCED BY POSITIVE LINEAR FUNCTIONALS
• Selfadjointness of ∗ -Representations Generated by Positive Linear Functionals
• A Noncommutative Probability Theory
• Topological properties of unbounded bicommutants
• On the Integral Representation of Positive Linear Functionals

This page was built for publication: An unbounded generalization of the Tomita-Takesaki theory