A Note on 2-Local Maps

Lin, Ying-Fen; Wong, Tsai–Lien

doi:10.1017/s0013091504001142

Cited by 36 publications

(25 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is proved that, given a commutative ring ℜ, an arbitrary 2-local inner derivation on M n (ℜ) is an inner derivation. This result extends the one obtained in [20] to the infinite dimensional case but for a commutative ring ℜ and in [1] to the case of a commutative ring but only for 2-local inner derivations.…”

Section: Introductionsupporting

confidence: 85%

2-Local derivations on associative and Jordan matrix rings over commutative rings

Ayupov

Arzikulov

2017

Linear Algebra and its Applications

View full text Add to dashboard Cite

Abstract. In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has an extension to a derivation on the matrix ring over this associative ring We also develop a Jordan analog of the above method and prove that every 2-local inner derivation on the Jordan matrix ring over a commutative ring is a derivation.

show abstract

Section: Introductionsupporting

confidence: 85%

2-Local derivations on associative and Jordan matrix rings over commutative rings

Ayupov

Arzikulov

2017

Linear Algebra and its Applications

View full text Add to dashboard Cite

show abstract

“…In 1997,Šemrl [7] introduced the notion of 2-local derivation and described 2-local derivations on the algebra B(H) of all bounded linear operators on the infinitedimensional separable Hilbert space H. A similar description for the finite-dimensional case appeared later in [5]. In the paper by Lin and Wong [6], 2-local derivations have been described on matrix algebras over finite-dimensional division rings.…”

Section: Introductionmentioning

confidence: 99%

2-Local Derivations on Semi-Finite Von Neumann Algebras

Ayupov¹,

Arzikulov²

2013

Glasgow Math. J.

View full text Add to dashboard Cite

show abstract

“…In the paper [8] 2-local derivations have been described on matrix algebras over finite-dimensional division rings.…”

mentioning

confidence: 99%

2-Local derivations on von Neumann algebras

Ayupov

Kudaybergenov

2014

Positivity

View full text Add to dashboard Cite

The paper is devoted to the description of 2-local derivations on von Neumann algebras. Earlier it was proved that every 2-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of Gleason Theorem for signed measures, we extend this result to type I I I von Neumann algebras. This implies that on arbitrary von Neumann algebra each 2-local derivation is a derivation.

show abstract

A Note on 2-Local Maps

Abstract: The aim of this note is to characterize 2-local automorphisms and derivations on matrix rings over finite-dimensional division rings.

Cited by 36 publications

References 11 publications

2-Local derivations on associative and Jordan matrix rings over commutative rings

2-Local derivations on associative and Jordan matrix rings over commutative rings

2-Local Derivations on Semi-Finite Von Neumann Algebras

2-Local derivations on von Neumann algebras

Contact Info

Product

Resources

About