Turkish Journal of Mathematics
DOI
10.3906/mat-1506-92
Abstract
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 $\mathcal{A}$ is a unital UMV-Banach algebra such that either $a = 0$ or $b = 0$ whenever $ab = 0$ in $\mathcal{A}$, and if $\delta:\mathcal{A} \rightarrow \mathcal{A}$ is a derivation such that $a \delta(a) = \delta(a)a$ for all $a \in \mathcal{A}$, then the following assertions are equivalent:\\ (i) $\delta$ is continuous; \\(ii) $\delta(e^a) = e^a\delta(a)$ for all $a \in \mathcal{A}$; \\(iii) $\delta$ is identically zero.
First Page
1058
Last Page
1070
Recommended Citation
HOSSEINI, AMIN
(2016)
"A characterization of derivations on uniformly mean value Banach algebras,"
Turkish Journal of Mathematics: Vol. 40:
No.
5, Article 12.
https://doi.org/10.3906/mat-1506-92
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss5/12
