Invariant $φ$-means on multiplier completion of Banach algebras with application to hypergroups

Mehdi Nemati; Maryam Rajaei Rizi

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arXiv · 1903.09875

Invariant $φ$-means on multiplier completion of Banach algebras with application to hypergroups

Mehdi Nemati·Maryam Rajaei Rizi

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Abstract

Let ${\mathcal A}$ be a Banach algebra and let $φ$ be a non-zero character on ${\mathcal A}$. Suppose that ${\mathcal A}_M$ is the closure of the faithful Banach algebra ${\mathcal A}$ in the multiplier norm. In this paper, topologically left invariant $φ$-means on ${\mathcal A}_M^*$ are defined and studied. Under some conditions on ${\mathcal A}$, we will show that the set of topologically left invariant $φ$-means on ${\mathcal A}^*$ and on ${\mathcal A}_M^*$ have the same cardinality. We also study the left uniformly continuous functionals associated with these algebras. The main applications are concerned with the Fourier algebra of an ultraspherical hypergroup $H$. In particular, we obtain some characterizations of discreteness of $H$.

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BibTeX RIS

Mehdi Nemati, Maryam Rajaei Rizi. 2019-03-23. Invariant $φ$-means on multiplier completion of Banach algebras with application to hypergroups. https://arxiv.org/abs/1903.09875

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