(p,H)-factorable operators on $L^{p}(G)$ for non-abelian groups

Abstract

For a locally compact group $G$ and a closed subgroup $H$ of $G$, we define the $(p, H)$-bracket product, which serves as a type of semi-inner product for $L^{p}(G)$. We proceed to investigate some of its properties. Additionally, we delve into the study of $(p, H)$-factorable operators and indicate the Riesz representation type theorem for this product, among other things.