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    Rights statement: The final, definitive version of this article has been published in the Journal, Journal of Functional Analysis 268 (8), 2015, © ELSEVIER.

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Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups

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Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups. / Choi, Yemon; Ghandehari, Mahya.

In: Journal of Functional Analysis, Vol. 268, No. 8, 15.04.2015, p. 2440-2463.

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Choi, Y & Ghandehari, M 2015, 'Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups', Journal of Functional Analysis, vol. 268, no. 8, pp. 2440-2463. https://doi.org/10.1016/j.jfa.2015.02.014

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Choi Y, Ghandehari M. Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups. Journal of Functional Analysis. 2015 Apr 15;268(8):2440-2463. https://doi.org/10.1016/j.jfa.2015.02.014

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Choi, Yemon ; Ghandehari, Mahya. / Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups. In: Journal of Functional Analysis. 2015 ; Vol. 268, No. 8. pp. 2440-2463.

Bibtex

@article{d359fca87c414b8badaca14a046e3a9d,
title = "Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups",
abstract = "A special case of a conjecture raised by Forrest and Runde (2005) [10] asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was already known to hold in the non-abelian compactcases, by earlier work of Johnson (1994) [13] and Plymen (unpublished note). In recent work (Choi and Ghandehari, 2014 [4]) the authors verified this conjecture for the real ax +b group and hence, by structure theory, for any semisimple Liegroup.In this paper we verify the conjecture for all 1-connected, non-abelian nilpotent Lie groups, by reducing the problem to the case of the Heisenberg group. As in our previous paper, an explicit non-zero derivation is constructed on a dense subalgebra, and then shown to be bounded using harmonic analysis. En route we use the known fusion rules for Schr{\"o}dinger representations to give a concrete realization of the “dual convolution” for this group as a kind of twisted,operator-valued convolution. We also give some partial results for solvable groups which give further evidence to support the general conjecture.",
keywords = "Dual convolution, Fourier algebra, Heisenberg group, Weak amenability",
author = "Yemon Choi and Mahya Ghandehari",
note = "The final, definitive version of this article has been published in the Journal, Journal of Functional Analysis 268 (8), 2015, {\textcopyright} ELSEVIER.",
year = "2015",
month = apr,
day = "15",
doi = "10.1016/j.jfa.2015.02.014",
language = "English",
volume = "268",
pages = "2440--2463",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "8",

}

RIS

TY - JOUR

T1 - Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups

AU - Choi, Yemon

AU - Ghandehari, Mahya

N1 - The final, definitive version of this article has been published in the Journal, Journal of Functional Analysis 268 (8), 2015, © ELSEVIER.

PY - 2015/4/15

Y1 - 2015/4/15

N2 - A special case of a conjecture raised by Forrest and Runde (2005) [10] asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was already known to hold in the non-abelian compactcases, by earlier work of Johnson (1994) [13] and Plymen (unpublished note). In recent work (Choi and Ghandehari, 2014 [4]) the authors verified this conjecture for the real ax +b group and hence, by structure theory, for any semisimple Liegroup.In this paper we verify the conjecture for all 1-connected, non-abelian nilpotent Lie groups, by reducing the problem to the case of the Heisenberg group. As in our previous paper, an explicit non-zero derivation is constructed on a dense subalgebra, and then shown to be bounded using harmonic analysis. En route we use the known fusion rules for Schrödinger representations to give a concrete realization of the “dual convolution” for this group as a kind of twisted,operator-valued convolution. We also give some partial results for solvable groups which give further evidence to support the general conjecture.

AB - A special case of a conjecture raised by Forrest and Runde (2005) [10] asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was already known to hold in the non-abelian compactcases, by earlier work of Johnson (1994) [13] and Plymen (unpublished note). In recent work (Choi and Ghandehari, 2014 [4]) the authors verified this conjecture for the real ax +b group and hence, by structure theory, for any semisimple Liegroup.In this paper we verify the conjecture for all 1-connected, non-abelian nilpotent Lie groups, by reducing the problem to the case of the Heisenberg group. As in our previous paper, an explicit non-zero derivation is constructed on a dense subalgebra, and then shown to be bounded using harmonic analysis. En route we use the known fusion rules for Schrödinger representations to give a concrete realization of the “dual convolution” for this group as a kind of twisted,operator-valued convolution. We also give some partial results for solvable groups which give further evidence to support the general conjecture.

KW - Dual convolution

KW - Fourier algebra

KW - Heisenberg group

KW - Weak amenability

U2 - 10.1016/j.jfa.2015.02.014

DO - 10.1016/j.jfa.2015.02.014

M3 - Journal article

VL - 268

SP - 2440

EP - 2463

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 8

ER -