Invariant projections and convolution operators
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- by Jacques Delaporte and Antoine Derighetti PDF
- Proc. Amer. Math. Soc. 129 (2001), 1427-1435 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1427-1435
- MSC (1991): Primary 43A15, 43A07; Secondary 43A45, 43A46, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-00-05874-3
- MathSciNet review: 1814169