Herz–Schur multiplier

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

$\mathrm{\Psi }:\sum _{g\in G}{\mu }_g{\lambda }_g\mapsto \sum _{g\in G}\psi (g){\mu }_g{\lambda }_g.$

See also

• Figà-Talamanca–Herz algebra
• Fourier algebra

References

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• Carl S. Herz. Une généralisation de la notion de transformée de Fourier-Stieltjes. Annales de l'Institut Fourier, tome 24, no 3 (1974), p. 145-157.

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