Abstract
In this short chapter, we discuss Schur multipliers restricted to various subspaces \(E \subset B(H)\). We first discuss the case when \(H = \ell_2\) 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 \(H = \ell_2(G)\) and E is the reduced C*-algebra \(C_{\lambda}^{*}(G)\), then the Schur multipliers which are completely bounded maps from E to E are identical to the completely bounded multipliers of \(C_{\lambda}^{*}(G)\) or equivalently to the (so-called) Herz-Schur multipliers of G.
Mathematics Subject Classification (2000):
- primary 47AO5
- 46LO5
- 43A65 secondary 47A20
- 47B 10
- 42B30
- 46E40
- 46L57
- 47C 15
- 47L20
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© 2001 Springer-Verlag Berlin/Heidelberg
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Pisier, G. (2001). 6. 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/10.1007/978-3-540-44563-0_7
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DOI: https://doi.org/10.1007/978-3-540-44563-0_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41524-4
Online ISBN: 978-3-540-44563-0
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