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Linear derivations on Banach algebras. (English) Zbl 1068.47039
In this interesting paper, the author proves that for an almost derivation on a Banach algebra, there exists a unique linear derivation near the derivation. Some applications are also given.

##### MSC:
 47B47 Commutators, derivations, elementary operators, etc. 39B82 Stability, separation, extension, and related topics for functional equations 47B48 Linear operators on Banach algebras 39B52 Functional equations for functions with more general domains and/or ranges 46K70 Nonassociative topological algebras with an involution 17C65 Jordan structures on Banach spaces and algebras 46L05 General theory of $$C^*$$-algebras
##### Keywords:
Hyers-Ulam stability; derivation; Banach algebras