Extensions of traces and type criterions for Jordan algebras of self- adjoint operators

DOI10.1007/BF01215023zbMath0477.46056MaRDI QIDQ1160871

Shavkat A. Ayupov

Publication date: 1982

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173231

zbMATH Keywords

enveloping von Neumann algebramodularitynormal faithful tracetraces on JW- algebrastype of a JW-algebratypes of JW-algebrasweakly closed Jordan algebras of self-adjoint operators

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Free probability and free operator algebras (46L54) General theory of von Neumann algebras (46L10) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Classifications of (C^*)-algebras (46L35) Jordan structures on Banach spaces and algebras (17C65)

Related Items (7)

Finite tripotents and finite \(\text{JBW}^\ast\)-triples ⋮ Extension of Jauch–Piron states on Jordan algebras ⋮ Conjugacy of involutive antiautomorphisms of von Neumann algebras ⋮ Jordan operator algebras ⋮ A new proof of the existence of traces on Jordan operator algebras and real von Neumann algebras ⋮ Convergences in JW-algebras and in their enveloping von Neumann algebras ⋮ Images of contractive projections on operator algebras

Cites Work

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• Tensor algebras over Hilbert spaces. II
• On normed Jordan algebras which are Banach dual spaces
• Real structure in the hyperfinite factor
• A Gelfand-Neumark theorem for Jordan algebras
• Jordan algebras of type I
• States of the Clifford algebra
• Derivatons of Jordan $C^*$-algebras.
• Positive projections and Jordan structure in operator algebras.
• On the Jordan Structure of C ∗ -Algebras
• Jordan algebras of self-adjoint operators
• Irreducible Jordan Algebras of Self-Adjoint Operators
• Jordan Algebras of Self-Adjoint Operators

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