Characterization of 2-Local Derivations and Local Lie Derivations on Some Algebras

被引：7
作者：
He, J. [1 ]
Li, J. [1 ]
An, G. [1 ]
Huang, W. [1 ]
机构：
[1] East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2018年 / 59卷 / 04期
基金：
中国国家自然科学基金;
关键词：
2-local derivation; local Lie derivation; 2-local Lie derivation; matrix algebra; von Neumann algebra; C-ASTERISK-ALGEBRAS; OPERATOR-ALGEBRAS; CSL ALGEBRAS; AUTOMORPHISMS; IDEALS;
D O I：
10.1134/S0037446618040146
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that each 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 each 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, the Jiang-Su algebra, and UHF algebras.
引用
收藏
页码：721 / 730
页数：10
相关论文
共 31 条
  • [1] Jordan derivations of full matrix algebras
    Alizadeh, R.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (01) : 574 - 578
  • [2] [Anonymous], 2006, ACTA MATH SIN CHIN S
  • [3] 2-Local derivations and automorphisms on B(H)
    Ayupov, Sh.
    Kudaybergenov, K.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 395 (01) : 15 - 18
  • [4] 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras
    Ayupov, Shavkat
    Kudaybergenov, Karimbergen
    [J]. ALGEBRA, ANALYSIS AND QUANTUM PROBABILITY, 2016, 697
  • [5] 2-Local derivations on von Neumann algebras
    Ayupov, Shavkat
    Kudaybergenov, Karimbergen
    [J]. POSITIVITY, 2015, 19 (03) : 445 - 455
  • [6] Local and 2-local derivations on noncommutative Arens algebras
    Ayupov, Shavkat
    Kudaybergenov, Karimbergen
    Nurjanov, Berdakh
    Alauadinov, Amir
    [J]. MATHEMATICA SLOVACA, 2014, 64 (02) : 423 - 432
  • [7] 2-LOCAL DERIVATIONS ON SEMI-FINITE VON NEUMANN ALGEBRAS
    Ayupov, Shavkat
    Arzikulov, Farkhad
    [J]. GLASGOW MATHEMATICAL JOURNAL, 2014, 56 (01) : 9 - 12
  • [8] Lie ideals: from pure algebra to C*-algebras
    Bresar, Matej
    Kissin, Edward
    Shulman, Victor S.
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 623 : 73 - 121
  • [9] Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces
    Chen, Lin
    Lu, Fangyan
    Wang, Ting
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2013, 77 (01) : 109 - 121
  • [10] Chen LS, 2015, J MED SYST, V39, DOI [10.1007/s10916-015-0333-0, 10.14177/j.cnki.32-1397n.2015.39.02.003]
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