Local and 2-local derivations on noncommutative Arens algebras
Shavkat AyupovThe Abdus Salam International Centre for Theoretical Physics (ICTP)Karimbergen KudaybergenovDepartment of Mathematics, Karakalpak State University, Ch. Abdirov 1, 230113, Nukus, UzbekistanB. O. NurjanovDepartment of Mathematics, Karakalpak State University, Ch. Abdirov 1, 230113, Nukus, UzbekistanAmir AlauadinovInstitute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Dormon yoli 29, 100125, Tashkent, Uzbekistan
ABI
Annotatsiya
Abstract The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra L ω(M,τ) associated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every 2-local derivation on L ω(M,τ) is a spatial derivation, and if M is a finite von Neumann algebra, then each local derivation on L ω(M,τ) is also a spatial derivation and every 2-local derivation on M is in fact an inner derivation.
Hali tarjima qilinmagan