Summary
In this short chapter, we discuss Schur multipliers restricted to various subspaces E ⊂ B(H). We first discuss the case when H = ℓ2 and E is the sub-class of all Hankel matrices. We show that the Schur multipliers which are completely bounded maps from E to E are closely related to the Fourier multipliers on the Hardy space H1. Analogously, when H = ℓ2(G) and E is the reduced C⋆ -algebra C⋆ λ(G), then the Schur multipliers which are completely bounded maps from E to E are identical to the completely bounded multipliers of C⋆ λ(G) or equivalently to the (so-called) Herz-Schur multipliers of G.
Keywords
- Discrete Group
- Fourier Multiplier
- Hankel Operator
- Hankel Matrice
- Lacunary Sequence
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© 1996 Springer-Verlag Berlin Heidelberg
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Pisier, G. (1996). Hankelian Schur multipliers. Herz-Schur multipliers. In: Similarity Problems and Completely Bounded Maps. Lecture Notes in Mathematics, vol 1618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21537-1_7
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DOI: https://doi.org/10.1007/978-3-662-21537-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60322-1
Online ISBN: 978-3-662-21537-1
eBook Packages: Springer Book Archive
