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Best bounds for the approximate units for certain ideals of $L^{1}(G)$ and of $A_{p}(G)$


Authors: Jacques Delaporte and Antoine Derighetti
Journal: Proc. Amer. Math. Soc. 124 (1996), 1159-1169
MSC (1991): Primary 43A20, 43A07; Secondary 22D15, 43A22, 46J10
DOI: https://doi.org/10.1090/S0002-9939-96-03130-9
MathSciNet review: 1301019
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Abstract: We compute the best bound for the approximate units of the augmentation ideal of the group algebra $L^{1}(G)$ of a locally compact amenable group $G$. More generally such a calculation is performed for the kernel of the canonical map from $L^{1}(G)$ onto $L^{1}(G/H)$, $H$ being a closed amenable subgroup of $G$. Analogous results involving certain ideals of the Fourier algebra of an amenable group are also discussed.


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Additional Information

Jacques Delaporte
Affiliation: Institut de Mathématiques, Faculté des Sciences, Université de Lausanne, CH-1015 Lausanne-Dorigny, Switzerland

Antoine Derighetti
Affiliation: Institut de Mathématiques, Faculté des Sciences, Université de Lausanne, CH-1015 Lausanne-Dorigny, Switzerland
Email: antoine.derighetti@ima.unil.ch

DOI: https://doi.org/10.1090/S0002-9939-96-03130-9
Keywords: Bounded approximate units, ideals, projections, amenable groups, Fourier algebra, Fig\`{a}-Talamanca Herz algebra
Received by editor(s): October 6, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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