Structure of derivations on various algebras of measurable operators for type I von Neumann algebras

DOI10.1016/j.jfa.2008.11.003zbMath1175.46054arXiv0808.0149OpenAlexW2126038653MaRDI QIDQ1019688

Shavkat A. Ayupov, Karimbergen K. Kudaybergenov, Sergio A. Albeverio

Publication date: 4 June 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.0149

zbMATH Keywords

von Neumann algebrasinner derivationderivationmeasurable operator\(\tau\)-measurable operatortype I von Neumann algebranoncommutative integrationlocally measurable operator

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Noncommutative measure and integration (46L51) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

Related Items

Ring isomorphisms of Murray-von Neumann algebras ⋮ Derivations, local and 2-local derivations on algebras of measurable operators ⋮ 2-local derivations on matrix algebras over commutative regular algebras ⋮ Continuous derivations on \(\ast\)-algebras of \(\tau\)-measurable operators are inner ⋮ Unnamed Item ⋮ Derivations with values in quasi-normed bimodules of locally measurable operators ⋮ Notes on derivations of Murray-von Neumann algebras ⋮ DERIVATIONS OF FRÉCHET NUCLEAR GB-ALGEBRAS ⋮ Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators ⋮ Ring derivations of Murray-von Neumann algebras ⋮ Non-existence of translation-invariant derivations on algebras of measurable functions ⋮ A note on commutator-simple algebras ⋮ Topologies on central extensions of von Neumann algebras ⋮ Continuity of derivations of algebras of locally measurable operators ⋮ Continuity of derivations on properly infinite \(*\)-algebras of \(\tau\)-measurable operators ⋮ Spatiality of derivations on the algebra of \(\tau \)-compact operators ⋮ Commutator estimates in \(W\)*-algebras ⋮ Spatiality of derivations of operator algebras in Banach spaces ⋮ Local derivations on subalgebras of \(\tau\)-measurable operators with respect to semi-finite von Neumann algebras ⋮ Local derivations on measurable operators and commutativity ⋮ Derivations with values in ideals of semifinite von Neumann algebras ⋮ Additive derivations on generalized Arens algebras ⋮ DERIVATIONS ON ALGEBRAS OF MEASURABLE OPERATORS ⋮ Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras ⋮ Characterizations of centralizable mappings on algebras of locally measurable operators ⋮ Spatiality of derivations of Fréchet GB$^{*}$-algebras ⋮ Derivations and 2-local derivations on matrix algebras and algebras of locally measurable operators ⋮ Derivations on Murray–von Neumann algebras ⋮ LOCAL DERIVATIONS ON ALGEBRAS OF MEASURABLE OPERATORS ⋮ Derivations of Murray-von Neumann algebras ⋮ Continuous derivations on algebras of locally measurable operators are inner ⋮ Derivations with values in the ideal of \(\tau\)-compact operators affiliated with a semifinite von Neumann algebra

Cites Work

• The Wickstead Problem
• Non-commutative Arens algebras and their derivations
• Cohomology of operator algebras. I: Type I von Neumann algebras
• On the algebra of measurable operators for a general \(AW^ *\)-algebra. II
• Algebras of type I
• A non-commutative extension of abstract integration
• Invariant measures on Boolean algebras
• Modules Over Operator Algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item