Herz-Schur multipliers and uniformly bounded representations of discrete groups

Bożejko, Marek; Fendler, Gero

doi:10.1007/bf01196860

Cited by 18 publications

(19 citation statements)

References 9 publications

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“…Then it follows [6] (or [49]) that u → 1 E n u is completely bounded on A(G). (We note that an alternative line of proof can be followed, using [7,Section 2] or [39,Section 2], by which we may see that sup n n cb 25. These proofs make use of the space T 1 (G) of Littlewood functions.)…”

Section: Remark 33mentioning

confidence: 99%

Completely bounded homomorphisms of the Fourier algebras

Ilie

Spronk

2005

Journal of Functional Analysis

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For locally compact groups G and H let A(G) denote the Fourier algebra of G and B(H ) the Fourier-Stieltjes algebra of H. Any continuous piecewise affine mapan element of the open coset ring) induces a completely bounded homomorphism : A(G) → B(H ) by setting u = u • on Y and u = 0 off of Y. We show that if G is amenable then any completely bounded homomorphism : A(G) → B(H ) is of this form; and this theorem fails if G contains a discrete nonabelian free group. Our result generalises results of Cohen (Amer.

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Section: Remark 33mentioning

confidence: 99%

Completely bounded homomorphisms of the Fourier algebras

Ilie

Spronk

2005

Journal of Functional Analysis

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“…This proposition is a concrete way to carry over to random forests the geometric aspects of a construction for free groups from [6], in accordance with the ideas expressed in the Introduction.…”

Section: Nonunitarizable Representations and Random Forests 4341mentioning

confidence: 76%

“…Such functions are called Littlewood functions (see e.g. [6,8,50]) in reference to classical harmonic analysis [32].…”

Section: Example 22mentioning

confidence: 99%

Nonunitarizable Representations and Random Forests

Epstein

Monod

2009

International Mathematics Research Notices

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Correspondence to be sent to: nicolas.monod@epfl.ch We establish a connection between Dixmier's unitarizability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is nonunitarizable if its first L 2 -Betti number is nonzero or if it is finitely generated with nontrivial cost. Our criterion also applies to torsion groups constructed by Osin, thus providing the first examples of nonunitarizable groups without free subgroups.

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“…The proof relies on the following two facts. (1) H 1 b (F, L ( 2 F)) = 0, see the proof of Theorem 2.7 * in [10], or [2]. (2) Every nonamenable countable group admits a free type II 1 action whose orbits contain the orbits of a free F-action [5], as described below.…”

Section: Proofsmentioning

confidence: 99%