Tensor preduals, positive homogeneity and harmonicity in two-Lipschitz spaces

Abstract

We study subspaces of two-Lipschitz mappings using group actions and tensor preduals. We first show that the ambient spaces contain large classical sequence spaces. We then use similarity actions to select smaller subspaces. Character-equivariant mappings form weak$^*$-closed fixed-point spaces and admit quotient tensor preduals. We give two applications. For mappings on Banach spaces, we describe positive homogeneity in each variable and construct bounded projections. For mappings on finitely generated groups, we characterize harmonicity in each variable. We show that the harmonic predual is the projective tensor product of the corresponding one-variable quotient preduals.