## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### A characterization of the $L^{\infty}$-representation algebra $\mathfrak{R}(S)$ of a foundation semigroup and its application to BSE algebras

Zeinab Kamali

#### Abstract

For a locally compact Hausdorff semigroup $S$, the $L^{\infty}$-representation algebra $\mathfrak{R}(S)$ was extensively studied by Dunkl and Ramirez. In this paper we give a characterization of the Banach algebra $\mathfrak{R}(S)$ of a foundation semigroup $S$ and as an application we determine some BSE semigroup algerbras.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 5 (2016), 59-63.

Dates
First available in Project Euclid: 28 April 2016

https://projecteuclid.org/euclid.pja/1461868541

Digital Object Identifier
doi:10.3792/pjaa.92.59

Mathematical Reviews number (MathSciNet)
MR3492813

Zentralblatt MATH identifier
1376.46038

#### Citation

Kamali, Zeinab. A characterization of the $L^{\infty}$-representation algebra $\mathfrak{R}(S)$ of a foundation semigroup and its application to BSE algebras. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 5, 59--63. doi:10.3792/pjaa.92.59. https://projecteuclid.org/euclid.pja/1461868541

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