Herz–Schur multiplier


In the mathematical field of representation theory, a Herz–Schur multiplier is a special kind of mapping from a group to the field of complex numbers.

Definition

Let Ψ be a mapping of a group G to the complex numbers. It is a Herz–Schur multiplier if the induced map Ψ: NN is a completely positive map, where N is the closure of the span M of the image of λ in B with respect to the weak topology, λ is the left regular representation of G and Ψ is on M defined as