Lebesgue-Fourier algebras on coset spaces and approximate amenability

Abstract

Let K be a compact subgroup of a locally compact group G. In this work, we initiate an investigation of the Lebesgue-Fourier algebra S¹ A(G/K) on the coset space G/K with pointwise multiplication; after some general results on the Banach algebra S¹ A(G/K), as our main result, we give some necessary conditions for that S¹ A(G/K) be approximately amenable in terms of algebraic and topological properties of G and K.