@inbook{6f78c79a7b284467b0bc62be903793e8,
title = "Derivations, local and 2-local derivations on algebras of measurable operators",
abstract = "The present paper presents a survey of some recent results devoted to derivations, local derivations and 2-local derivations on various algebras of measurable operators affiliated with von Neumann algebras. We give a complete description of derivation on these algebras, except the case where the von Neumann algebra is of type II1. In the latter case the result is obtained under an extra condition of measure continuity of derivations. Local and 2-local derivations on the above algebras are also considered. We give sufficient conditions on a von Neumann algebra M, under which every local or 2-local derivation on the algebra of measurable operators affiliated with M is automatically becomes a derivation. We also give examples of commutative algebras of measurable operators admitting local and 2-local derivations which are not derivations.",
keywords = "2-local derivation, Central extensions of von Neumann algebras, Inner derivation, Local derivations, Locally measurable operator, Measurable operator, Regular algebra, Spatial derivation, von Neumann algebras",
author = "Shavkat Ayupov and Karimbergen Kudaybergenov",
note = "Publisher Copyright: {\textcopyright} 2016 American Mathematical Society.",
year = "2016",
doi = "10.1090/conm/672/13468",
language = "英语",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "51--72",
booktitle = "Contemporary Mathematics",
address = "美国",
}