Geodesic
On uniformly continuous operators and some weight-hyperbolic function Banach algebra
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 393-401 
Ana L. Barrenechea; Carlos C. Peña. On uniformly continuous operators and some weight-hyperbolic function Banach algebra. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 393-401. http://geodesic.mathdoc.fr/item/SEMR_2006_3_a26/
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     title = {On uniformly continuous operators and some weight-hyperbolic function {Banach} algebra},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider an abelian non-unitary Banach algebra $\mathfrak{A}$, ruled by an hyperbolic weight, defined on certain space of Lebesgue measurable complex valued functions on the positive axis. Since the non-convolution Banach algebra $\mathfrak{A}$ has its own interest by its applications to the representation theory of some Lie groups, we search on various of its properties. As a Banach space, $\mathfrak{A}$ does not have the Radon–Nikodým property. So, it could be exist not representable linear bounded operators on $\mathfrak{A}$ (cf. [6]). However, we prove that the class of locally absolutely continuous bounded operators are representable and we determine their kernels.

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