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
- Figà-Talamanca–Herz algebra
- Fourier algebra
References
- Pisier, Gilles (1995), "Multipliers and lacunary sets in non-amenable groups", American Journal of Mathematics, The Johns Hopkins University Press, 117 (2): 337–376, arXiv:math/9212207
, doi:10.2307/2374918, ISSN 0002-9327, JSTOR 2374918, MR 1323679 - Figà-Talamanca, Alessandro; Picardello, Massimo A. (1983), Harmonic analysis on free groups, Lecture Notes in Pure and Applied Mathematics, 87, New York: Marcel Dekker Inc., ISBN 978-0-8247-7042-6, MR 710827
- 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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