A characterization of derivations on uniformly mean value Banach algebras | Zendy

Amin Hosseini | Zendy

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A characterization of derivations on uniformly mean value Banach algebras

Author(s) -

Amin Hosseini

Publication year - 2016

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1506-92

Subject(s) - banach algebra , mathematics , class (philosophy) , unital , pure mathematics , zero (linguistics) , characterization (materials science) , discrete mathematics , banach space , combinatorics , algebra over a field , physics , linguistics , philosophy , optics , artificial intelligence , computer science

In this paper, a uniformly mean value Banach algebra (briefly UMV-Banach algebra) is defined as a new class of Banach algebras, and we characterize derivations on this class of Banach algebras. Indeed, it is proved that if A is a unital UMV-Banach algebra such that either a = 0 or b = 0 whenever ab = 0 in A , and if δ : A → A is a derivation such that aδ(a) = δ(a)a for all a ∈ A , then the following assertions are equivalent: (i) δ is continuous; (ii) δ(e) = eδ(a) for all a ∈ A ; (iii) δ is identically zero.

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