Article

# Additive derivations on generalized Arens algebras

Lobachevskii Journal of Mathematics 10/2010; DOI: 10.1134/S1995080211030024

Source: arXiv

- Citations (19)
- Cited In (0)

- [Show abstract] [Hide abstract]

**ABSTRACT:**Given a von Neumann algebra $M$ we introduce so called central extension $mix(M)$ of $M$. We show that $mix(M)$ is a *-subalgebra in the algebra $LS(M)$ of all locally measurable operators with respect to $M,$ and this algebra coincides with $LS(M)$ if and only if $M $ does not admit type II direct summands. We prove that if $M$ is a properly infinite von Neumann algebra then every additive derivation on the algebra $mix(M)$ is inner. This implies that on the algebra $LS(M)$, where $M$ is a type I$_\infty$ or a type III von Neumann algebra, all additive derivations are inner derivations.JOURNAL OF OPERATOR THEORY 05/2012; 67(2):495-510. · 0.50 Impact Factor -
- [Show abstract] [Hide abstract]

**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.Infinite Dimensional Analysis Quantum Probability and Related Topics 09/2009; 13(2):305-337. · 0.65 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.