Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces

Chen, Lin; Lu, Fangyan; Wang, Ting

doi:10.1007/s00020-013-2074-0

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Introduction4

More Generally a Linear Map δ Of U Is Called A Lie Derivation If δ([A B]) = [δ(A) B] + [A δ(B)]1

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2015

2024

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Cited by 25 publications

(9 citation statements)

References 23 publications

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“…Then the following question seem natural: What is the structure of local Lie derivations? Chen et al [4] consider the questions on the algebra B(X ) of all bounded linear operators on Banach space X . They showed that each local Lie derivation from B(X ) into itself is a Lie derivation.…”

Section: More Generally a Linear Map δ Of U Is Called A Lie Derivation If δ([A B]) = [δ(A) B] + [A δ(B)]mentioning

confidence: 99%

On local Lie derivations of generalized matrix algebras

Liu

2019

Banach J. Math. Anal.

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Section: More Generally a Linear Map δ Of U Is Called A Lie Derivation If δ([A B]) = [δ(A) B] + [A δ(B)]mentioning

confidence: 99%

On local Lie derivations of generalized matrix algebras

Liu

2019

Banach J. Math. Anal.

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“…A linear map δ of an algebra A is called a local Lie derivation if, for each A ∈ A, there exists a Lie derivation δ A such that δ(A) = δ A (A). In [1], the authors studied local Lie derivations of operator algebras on Banach spaces. In this paper, as the continuity of the previous work, we study the local Lie derivations of nest algebras on Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Local Lie derivations of nest algebras

Chen

2015

Linear Algebra and its Applications

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“…[13,Theorem 7.5]). Based on these results, many authors have studied local derivations on operator algebras, for example, see in [2,3,4,5,6,7,8,9,10,11,12,15,16,17,18,19,20,22,23].…”

Section: Introductionmentioning

confidence: 99%

Local derivations on associative and Jordan matrix algebras

Ayupov¹,

Arzikulov²,

Umrzaqov³

2019

UzMJ

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In the present paper we prove that every additive (not necessarily homogenous) local inner derivation on the algebra of matrices over an arbitrary field is an inner derivation, and every local inner derivation on the ring of matrices over a finite ring generated by the identity element or the ring of integers is an inner derivation. We also prove that every additive local inner derivation on the Jordan algebra of symmetric matrices over an arbitrary field is a derivation, and every local inner derivation on the Jordan ring of symmetric matrices over a finite ring generated by the identity element or the ring of integers is a derivation.

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Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces

Cited by 25 publications

References 23 publications

On local Lie derivations of generalized matrix algebras

On local Lie derivations of generalized matrix algebras

Local Lie derivations of nest algebras

Local derivations on associative and Jordan matrix algebras

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