Rights statement: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, [266, 11, (2014)] DOI: 10.1016/j.jfa.2014.03.012
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Weak and cyclic amenability for Fourier algebras of connected Lie groups
AU - Choi, Yemon
AU - Ghandehari, Mahya
N1 - NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, [266, 11, (2014)] DOI: 10.1016/j.jfa.2014.03.012
PY - 2014/6/1
Y1 - 2014/6/1
N2 - Using techniques of non-abelian harmonic analysis, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the real ax+b group. In particular this provides the first proof that this algebra is not weakly amenable. Using the structure theory of Lie groups, we deduce that the Fourier algebras of connected, semisimple Lie groups also support non-zero, cyclic derivations and are likewise not weakly amenable. Our results complement earlier work of Johnson (JLMS, 1994), Plymen (unpublished note) and Forrest–Samei–Spronk (IUMJ, 2009). As an additional illustration of our techniques, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the reduced Heisenberg group, providing the first example of a connected nilpotent group whose Fourier algebra is not weakly amenable.
AB - Using techniques of non-abelian harmonic analysis, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the real ax+b group. In particular this provides the first proof that this algebra is not weakly amenable. Using the structure theory of Lie groups, we deduce that the Fourier algebras of connected, semisimple Lie groups also support non-zero, cyclic derivations and are likewise not weakly amenable. Our results complement earlier work of Johnson (JLMS, 1994), Plymen (unpublished note) and Forrest–Samei–Spronk (IUMJ, 2009). As an additional illustration of our techniques, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the reduced Heisenberg group, providing the first example of a connected nilpotent group whose Fourier algebra is not weakly amenable.
KW - Coefficient functions
KW - Cyclic amenability
KW - Derivations
KW - Fourier algebra
KW - Lie group
KW - Square-integrable representation
KW - Weak amenability
U2 - 10.1016/j.jfa.2014.03.012
DO - 10.1016/j.jfa.2014.03.012
M3 - Journal article
VL - 266
SP - 6501
EP - 6530
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 11
ER -