The Fourier algebra of SL(2,?) ? ? n ,n ? 2, has no multiplier bounded approximate unit

Brian Dorofaeff

doi:10.1007/bf01459526

The Fourier algebra of SL(2,?) ? ? n ,n ? 2, has no multiplier bounded approximate unit

Mathematische Annalen ◽

10.1007/bf01459526 ◽

1993 ◽

Vol 297 (1) ◽

pp. 707-724 ◽

Cited By ~ 10

Author(s):

Brian Dorofaeff

Keyword(s):

Fourier Algebra ◽

Approximate Unit

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Completely bounded bimodule maps and spectral synthesis

International Journal of Mathematics ◽

10.1142/s0129167x17500677 ◽

2017 ◽

Vol 28 (10) ◽

pp. 1750067 ◽

Cited By ~ 2

Author(s):

M. Alaghmandan ◽

I. G. Todorov ◽

L. Turowska

Keyword(s):

Tensor Product ◽

Compact Group ◽

Closed Subset ◽

Spectral Synthesis ◽

Locally Compact Group ◽

Product Formula ◽

Fourier Algebra ◽

Locally Compact ◽

Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

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Canadian Journal of Mathematics ◽

10.4153/cjm-2004-055-8 ◽

2004 ◽

Vol 56 (6) ◽

pp. 1259-1289 ◽

Cited By ~ 5

Author(s):

Alan L. T. Paterson

Keyword(s):

Duality Theorem ◽

Locally Compact Groups ◽

Compact Groups ◽

Fourier Algebra ◽

Hilbert Modules ◽

Locally Compact ◽

Classical Duality ◽

Special Case

AbstractWe introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.

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