Elements of Tomita-Takesaki theory for embeddable \(AW^*\)-algebras

DOI10.1007/BF00127862zbMath0647.46048OpenAlexW2003112564MaRDI QIDQ1104522

Michael Frank

Publication date: 1989

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00127862

zbMATH Keywords

one-parameter groupfaithful self-dual Hilbert \(C^*\)-modulegeneralized K.M.S. conditionlocally trivial Hilbert bundles on Stoneian basic spacesTomita-Takesaki theory for embeddable \(AW^*\)-algebras

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Cites Work

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• A classification of type I \(AW^*\)-algebras and Boolean valued analysis
• A bounded operator approach to Tomita-Takesaki theory
• Tomita's theory of modular Hilbert algebras and its applications
• Projections in Banach algebras
• Embedding AW^∗ -Algebras as Double Commutants in Type I Algebras
• Embeddable AW^∗ -Algebras and Regular Completions
• Kaplansky-Hilbert Modules and the Self-Adjointness Of Operator Algebras
• The Double B-Dual Of An Inner Product Module Over a C*-Algebra B
• Linear Operators in VH-Spaces
• A Spectral Theorem for Normal Operators on a Kaplansky-Hilbert Module
• Representations of algebras by continuous sections
• Inner Product Modules Over B ∗ -Algebras
• Modules Over Operator Algebras

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