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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invariant projections and convolution operators


Authors: Jacques Delaporte and Antoine Derighetti
Journal: Proc. Amer. Math. Soc. 129 (2001), 1427-1435
MSC (1991): Primary 43A15, 43A07; Secondary 43A45, 43A46, 46J10
Published electronically: October 25, 2000
MathSciNet review: 1814169
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Abstract:

We prove the existence of invariant projections $\mathcal{P}$ from the Banach space $PM_{p}(G)$ of $p$-pseudomeasures onto $PM_{p}(H)$ with $\operatorname{supp} {\mathcal{P}}(T)\subset \operatorname{supp}T$ for $H$ closed neutral subgroup of a locally compact group $G$. As a main application we obtain that every closed neutral subgroup is a set of $p$-synthesis in $G$ and in fact locally $p$-Ditkin in $G$. We also obtain an extension theorem concerning the Fourier algebra.


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Additional Information

Jacques Delaporte
Affiliation: Institut de Mathématiques, Faculté des Sciences, Université de Lausanne, CH-1015 Lausanne-Dorigny, Switzerland
Email: jdelaporte@mail.vtx.ch

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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05874-3
PII: S 0002-9939(00)05874-3
Keywords: Convolution operators, pseudomeasures, amenable groups, spectral synthesis, Ditkin sets, Fourier algebra, Fig\`{a}-Talamanca Herz algebra
Received by editor(s): August 17, 1999
Published electronically: October 25, 2000
Additional Notes: This work was supported by the Swiss National Science Foundation
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society