Derivations on the algebra of τ-compact operators affiliated with a type i von Neumann algebra

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

doi:10.1007/s11117-007-2107-5

Derivations on the algebra of τ-compact operators affiliated with a type i von Neumann algebra

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

^*Corresponding author for this work

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

6 Scopus citations

Abstract

Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S ₀(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S ₀(M, τ) is spatial and generated by an element from L(M, τ).

Original language	English
Pages (from-to)	375-386
Number of pages	12
Journal	Positivity
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s11117-007-2107-5
State	Published - May 2008
Externally published	Yes

Keywords

Derivation
Inner derivation
Kaplansky-Hilbert module
Measurable operator
Measure topology
Non commutative integration
Spatial derivation
Type I algebra
Von Neumann algebras
τ-compact operator

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10.1007/s11117-007-2107-5

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title = "Derivations on the algebra of τ-compact operators affiliated with a type i von Neumann algebra",

abstract = "Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S 0(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S 0(M, τ) is spatial and generated by an element from L(M, τ).",

keywords = "Derivation, Inner derivation, Kaplansky-Hilbert module, Measurable operator, Measure topology, Non commutative integration, Spatial derivation, Type I algebra, Von Neumann algebras, τ-compact operator",

author = "Sergio Albeverio and Ayupov, \{Shavkat A.\} and Kudaybergenov, \{Karimbergen K.\}",

year = "2008",

month = may,

doi = "10.1007/s11117-007-2107-5",

language = "英语",

volume = "12",

pages = "375--386",

journal = "Positivity",

issn = "1385-1292",

publisher = "Springer International Publishing",

number = "2",

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TY - JOUR

T1 - Derivations on the algebra of τ-compact operators affiliated with a type i von Neumann algebra

AU - Albeverio, Sergio

AU - Ayupov, Shavkat A.

AU - Kudaybergenov, Karimbergen K.

PY - 2008/5

Y1 - 2008/5

N2 - Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S 0(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S 0(M, τ) is spatial and generated by an element from L(M, τ).

AB - Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S 0(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S 0(M, τ) is spatial and generated by an element from L(M, τ).

KW - Derivation

KW - Inner derivation

KW - Kaplansky-Hilbert module

KW - Measurable operator

KW - Measure topology

KW - Non commutative integration

KW - Spatial derivation

KW - Type I algebra

KW - Von Neumann algebras

KW - τ-compact operator

UR - https://www.scopus.com/pages/publications/43149086013

U2 - 10.1007/s11117-007-2107-5

DO - 10.1007/s11117-007-2107-5

M3 - 文章

AN - SCOPUS:43149086013

SN - 1385-1292

VL - 12

SP - 375

EP - 386

JO - Positivity

JF - Positivity

IS - 2

ER -

Derivations on the algebra of τ-compact operators affiliated with a type i von Neumann algebra

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Keywords

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