Weak 2-local derivations on \mathbbM_n

2015/03/04 by Mohsen Niazi, Niazi, Mohsen, Antonio M. Peralta +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1503.01346

arxiv created 2015/03/04 · openalex publication_date 2015/03/04 · arxiv updated 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of weak-2-local derivation (respectively, ^*-derivation) on a C^*-algebra A as a (non-necessarily linear) map Δ: A→ A satisfying that for every a,b∈ A and ϕ∈ A^* there exists a derivation (respectively, a ^*-derivation) D_a,b,ϕ: A→ A, depending on a, b and ϕ, such that ϕΔ(a) = ϕD_a,b,ϕ (a) and ϕΔ(b) = ϕD_a,b,ϕ (b). We prove that every weak-2-local ^*-derivation on M_n is a linear derivation. We also show that the same conclusion remains true for weak-2-local ^*-derivations on finite dimensional C^*-algebras.

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