Boolean Valued Analysis: Background and Results

DOI10.1007/978-3-030-49763-7_9zbMath1482.06003OpenAlexW3119503949MaRDI QIDQ5013599

Anatoly G. Kusraev, Semen S. Kutateladze

Publication date: 2 December 2021

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-49763-7_9

zbMATH Keywords

vector latticeBoolean valued analysisGordon's theoremBoolean valued representationKantorovich's principle

Mathematics Subject Classification ID

Ordered rings, algebras, modules (06F25) Ordered topological linear spaces, vector lattices (46A40) Nonclassical models (Boolean-valued, sheaf, etc.) (03C90)

Cites Work

• Classification of injective Banach lattices
• Boolean valued interpretation of Hilbert space theory
• Boolean-linear spaces
• Concerning problem 18 from Goodearl's book ``Von Neumann regular rings
• Atomic decomposition of vector measures
• Theorems on preservation of relations in K-spaces
• Order-continuous functionals in Boolean-valued models of set theory
• An approach to the dimension theory of continuous geometry from the standpoint of Boolean valued analysis
• Banach-Kantorovich spaces
• Boolean valued analysis and type I \(AW^*\)-algebras
• Some applications of Boolean valued set theory to abstract harmonic analysis on locally compact groups
• A classification of type I \(AW^*\)-algebras and Boolean valued analysis
• Von Neumann algebras and Boolean valued analysis
• Banach lattices
• On the Strassen disintegration theorem
• On abstract \(JW\)-algebras
• Boolean-valued analysis and injective Banach lattices
• Order-continuous extension of a positive operator
• Boolean-valued analysis and \(JB\)-algebras
• Locally one-dimensional \(K\)-spaces and \(\sigma\)-distributive Boolean algebras
• On the structure of \(AJW\)-algebras of type \(I_2\)
• Two applications of Boolean valued analysis
• A model of set-theory in which every set of reals is Lebesgue measurable
• Lectures in set theory with particular emphasis on the method of forcing
• Iterated Cohen extensions and Souslin's problem
• Projections in Banach algebras
• A Transfer Principle from Von Neumann Algebras to AW^∗ -Algebras
• Hilbert Space Methods in the Theory of Lie Algebras
• Boolean Valued Dedekind Domains
• Problems of set-theoretic non-standard analysis
• Abstract Theory of Abelian Operator Algebras: An Application of Forcing
• Boolean Valued Analysis Approach to the Trace Problem of Aw∗-Algebras
• Embeddable AW^∗ -Algebras and Regular Completions
• First Order Theory of Complete Stonean Algebras (Boolean-Valued Real and Complex Numbers)
• Boolean simple groups and boolean simple rings
• A transfer principle in harmonic analysis
• Boolean valued Lie algebras
• Extensions of positive operators between Banach lattices
• Extensions and Liftings of Positive Linear Mappings on Banach Lattices
• Two Applications of Logic to Mathematics
• A boolean transfer principle from L*‐Algebras to AL*‐Algebras
• Jordan algebras of self-adjoint operators
• Vector Measures.
• Boolean valued interpretation of Banach space theory and module structures of von Neumann algebras
• Modules Over Operator Algebras
• Une Caracterisation Vectorielle-Metrique Des Espaces L¹
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