With every locally compact group $G$, one can associate several interesting bi-invariant subspaces $X(G)$ of the weakly almost periodic functions $\mathrm{WAP}(G)$ on each which captures parts representation theory $G$. Under certain natural assumptions, such a space carries unique invariant mean and has predual, we view weak$^*$-continuity this as rigidity property Important examples spaces $X...

Let m(a, b) and M(a, b, c) be symmetric means. We say that M is type 1 invariant with respect to m if M(m(a, c),m(a, b),m(b, c)) ≡ M(a, b, c). If m is strict and isotone, then we show that there exists a unique M which is type 1 invariant with respect to m. In particular we discuss the invariant logarithmic mean L3, which is type 1 invariant with respect to L(a, b) = b−a log b−log a . We say th...

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...