Cohomology of the (Fourier) Lebesgue-Fourier Algebras on Coset Spaces of Locally Compact Groups

Document Type : Original Article

Author

Maryam Esfandani

Department of Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan 84156-83111‎, ‎Iran.

10.22034/kjm.2025.492333.3395

Abstract

‎For a compact subgroup $K$ of a locally compact group $G$‎, ‎we describe the multiplier algebra of the (Fourier) Lebesgue--Fourier algebra on the coset space $G/K$‎. ‎This allows us to compare and study the multiplier-bounded approximate identity of the Lebesgue--Fourier algebra and the Fourier algebra on $G/K$‎. ‎Moreover‎, ‎characterizing the multiplier algebra of a commutative semisimple regular Banach algebra $\mathcal{A}$ with the Gelfand structure space $X$‎, ‎we show that‎ if $\mathcal{A}$ has a multiplier-bounded approximate identity and $\mathcal{A}$ is approximately amenable‎, ‎then the norm on $\mathcal{A}$ is equivalent to the norm on its multiplier algebra‎. Additionally‎, ‎we investigate some cohomological properties of the (Fourier) Lebesgue--Fourier algebra with a multiplier-bounded approximate identity on $G/K$‎. ‎Furthermore‎, ‎we examine certain hereditary properties of amenability‎, ‎approximate amenability‎, ‎pseudo-amenability‎, ‎and weak amenability of the Fourier algebra on $G/K$‎.

Keywords

Locally compact group

Lebesgue-Fourier algebra

coset space

amenability

multiplier algebra

Subjects

• 43 Abstract harmonic analysis

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