Ayupov, Shavkat; Kudaybergenov, Karimbergen; Nurjanov, Berdakh; Alauadinov, Amir Local and 2-local derivations on noncommutative Arens algebras. (English) Zbl 1349.46071 Math. Slovaca 64, No. 2, 423-432 (2014). Let \(M\) be a von Neumann algebra with faithful normal semi-finite trace \(\tau \). Denote by \(L^\omega (M,\tau)\) the corresponding Arens algebra which is the intersection of all spaces \(L^p (M,\tau)\), \(p\geq 1\). The authors prove that every (a priori nonlinear) 2-local derivation on \(L^\omega (M,\tau)\) is a spatial derivation. If \(M\) is finite, then the linear local derivations on \(L^\omega (M,\tau)\) are also spatial derivations and every 2-local derivation is in fact an inner derivation. Reviewer: Lajos Molnár (Debrecen) Cited in 16 Documents MSC: 46L52 Noncommutative function spaces 46L51 Noncommutative measure and integration Keywords:von Neumann algebra; semi-finite trace; noncommutative Arens algebra; derivation; local derivation; 2-local derivation PDFBibTeX XMLCite \textit{S. Ayupov} et al., Math. Slovaca 64, No. 2, 423--432 (2014; Zbl 1349.46071) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.