Derivations on algebras of measurable operators

Sh A. Ayupov; K. K. Kudaybergenov

doi:10.1142/S0219025710004085

Derivations on algebras of measurable operators

Sh A. Ayupov
, K. K. Kudaybergenov

Academy of Sciences of the Republic of Uzbekistan
Karakalpak State University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The present paper is a survey of recent results concerning derivations on various algebras of measurable operators affiliated with von Neumann algebras. A complete description of derivation is obtained in the case of type I von Neumann algebras. A special section is devoted to the Abelian case, namely to the existence of nontrivial derivations on algebras of measurable function. Local derivations on the above algebras are also considered.

Original language	English
Pages (from-to)	305-337
Number of pages	33
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	13
Issue number	2
DOIs	https://doi.org/10.1142/S0219025710004085
State	Published - Jun 2010
Externally published	Yes

Keywords

central extensions of von Neumann algebras
derivation
inner derivation
local derivation
locally measurable operator
measurable operator
noncommutative Arens algebras
regular algebra
spatial derivation
von Neumann algebras

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abstract = "The present paper is a survey of recent results concerning derivations on various algebras of measurable operators affiliated with von Neumann algebras. A complete description of derivation is obtained in the case of type I von Neumann algebras. A special section is devoted to the Abelian case, namely to the existence of nontrivial derivations on algebras of measurable function. Local derivations on the above algebras are also considered.",

keywords = "central extensions of von Neumann algebras, derivation, inner derivation, local derivation, locally measurable operator, measurable operator, noncommutative Arens algebras, regular algebra, spatial derivation, von Neumann algebras",

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AB - The present paper is a survey of recent results concerning derivations on various algebras of measurable operators affiliated with von Neumann algebras. A complete description of derivation is obtained in the case of type I von Neumann algebras. A special section is devoted to the Abelian case, namely to the existence of nontrivial derivations on algebras of measurable function. Local derivations on the above algebras are also considered.

KW - central extensions of von Neumann algebras

KW - derivation

KW - inner derivation

KW - local derivation

KW - locally measurable operator

KW - measurable operator

KW - noncommutative Arens algebras

KW - regular algebra

KW - spatial derivation

KW - von Neumann algebras

UR - https://www.scopus.com/pages/publications/77954599547

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M3 - 文章

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JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

IS - 2

ER -

Derivations on algebras of measurable operators

Abstract

Keywords

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