A Class of compact operators on homogeneous spaces

Let ϖ be a representation of the homogeneous space G/H, where G be a locally compact group and H be a compact subgroup of G. For an admissible wavelet ζ for ϖ and ψ∈Lp(G/H), 1≤p<∞, we determine a class of bounded compact operators which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators

On the Topological Centre of L1(G/H)∗∗L^1(G/H)^{\ast\ast}

Let $G$ be a locally compact group and $H$ be a compact subgroup of $G$. Using a general criterion established by Neufang in \cite{Neuf} we show that the Banach algebra $L^1(G/H)$ is Arens irregular for a large class of locally compact groups. DOI: 10.1017/S000497271200012