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Local and 2-local derivations on noncommutative Arens algebras. (English) Zbl 1349.46071

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.

MSC:

46L52 Noncommutative function spaces
46L51 Noncommutative measure and integration
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