Characterizations of 2-local derivations and local Lie derivations on some algebras

2016/11/05 by Jun He, Jiankui Li, He, Jun +5
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1611.01632

openalex publication_date 2016/11/05 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28

Abstract

We prove that every 2-local derivation from the algebra M_n(A)(n>2) into its bimodule M_n(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie derivations on some algebras such as von Neumann algebras, nest algebras, Jiang-Su algebra and UHF algebras.

Related

• 2-Local derivations on matrix algebras and algebras of measurable operators
• Derivations and 2-local derivations on matrix algebras over commutative algebras
• 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW^∗-algebras
• Local Lie n-derivations on certain algebras
• Local Lie derivations on von Neumann algebras and algebras of locally measurable operators