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
See also
References
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- S2CID 2958712
- Figà-Talamanca, Alessandro; Picardello, Massimo A. (1983), Harmonic analysis on free groups, Lecture Notes in Pure and Applied Mathematics, vol. 87, New York: Marcel Dekker Inc., MR 0710827
- 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.