On geometric properties of ${\mathrm{\ell }}^p$-spaces on unitary duals of compact groups

In this paper, we study geometric properties of ${\mathrm{\ell }}^p$-spaces associated with the unitary dual of a compact group. More precisely, we prove uniform smoothness, uniform convexity, Clarkson type inequalities, Kadec-Klee property, as well as type and cotype properties of such spaces. We also present duality and complex interpolation results.