In the mathematical field of representation theory, a Herz–Schur multiplier (named after Carl S. Herz and Issai Schur) 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: "N"("G") → "N"("G") is a completely positive map, where "N"("G") is the closure of the span "M" of the image of λ in "B"("ℓ" 2("G")) with respect to the weak topology, λ is the left regular representation of "G" and Ψ is on "M" defined as
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