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April 2022 Weakly compact multipliers and φ-amenable Banach algebras
Mehdi Nemati, Zhila Sohaei
Rocky Mountain J. Math. 52(2): 695-705 (April 2022). DOI: 10.1216/rmj.2022.52.695

Abstract

Let 𝒜 be a Banach algebra and let J be a closed ideal of 𝒜 such that φ|J0 for some nonzero character φ on 𝒜. We obtain some relations between the existence of compact and weakly compact multipliers on J and on 𝒜 in some sense. Then we apply these results to hypergroup algebra L1(K) when K is a locally compact hypergroup. In particular, for a closed ideal J in L1(K) we prove that K is compact if and only if there is fJ such that φ1(f)0 and the multiplication operator λf:ggf is weakly compact on J. Using this, we study Arens regularity of J whenever it has a bounded left approximate identity. Finally, we apply these results on some abstract Segal algebras with respect to the L1(K).

Citation

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Mehdi Nemati. Zhila Sohaei. "Weakly compact multipliers and φ-amenable Banach algebras." Rocky Mountain J. Math. 52 (2) 695 - 705, April 2022. https://doi.org/10.1216/rmj.2022.52.695

Information

Received: 14 February 2021; Revised: 12 July 2021; Accepted: 9 August 2021; Published: April 2022
First available in Project Euclid: 17 May 2022

Digital Object Identifier: 10.1216/rmj.2022.52.695

Subjects:
Primary: 43A22 , 46H20
Secondary: ‎43A07‎ , 43A62

Keywords: (weakly) compact multiplier , abstract Segal algebra , Arens regularity , Hypergroup , φ-amenability

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 2 • April 2022
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