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.
Keywords
Derivation, mean value property, uniformly mean value property, classical mean value theorem, Gelfand transform
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
