Note that a k- mean on a topological space $X$ is a continuous function $f:X^{k}\to X$ which is identity on the diagonal and is invariant under permutations.

In the literature is there an appropriate analogy of concept "mean" in the context of commutative Banach algebra? That is a morphism $\alpha:A\to A\otimes A$ which is invariant under flip-operator and its composition with mutiplicative operator would be identity. (with respect to an appropriate norm tensor product). (And the generalization to k-fold tensor product). Please see the attached file for a topological mean.