Strongly generalized derivations on C*-algebras

2025/09/08 by Amin Hosseini, Hosseini, Amin
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 46H40 #Secondary 47B47

paper · pdf · doi:10.48550/arxiv.2509.06634

openalex publication_date 2025/09/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

Let A and B be two algebras, let M be a B-bimodule and let n be a positive integer. A linear mapping D_n:A → M is called a strongly generalized derivation of order n, if there exist the families \E_k:A → M\_{k = 1}ⁿ, \H_k:A → M\_{k = 1}ⁿ, \F_k:A → B\_{k = 1}ⁿ and \G_k:A → B\_{k = 1}ⁿ of mappings which satisfy D_n(ab) = ∑_{k = 1}ⁿ[E_k(a) F_k(b) + G_k(a)H_k(b)] for all a, b ∈ A. In this paper, we prove that every strongly generalized derivation of order one from a C^∗-algebra into a Banach bimodule is automatically continuous under certain conditions. The main theorem of this paper extends some celebrated results in this regard.

Citations

• On the equivalence of all notions of generalized derivations whose domain is a C^∗-algebra
• Linear maps on C*-algebras which are derivations or triple derivations\n at a point
• Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras

Related

• Automatic continuity of new generalized derivations
• On the equivalence of all notions of generalized derivations whose domain is a C^∗-algebra
• Nearly generalized Jordan derivations
• Weak-local derivations and homomorphisms on C*-algebras
• Cubic Derivations on Banach Algebras