Transference and preservation of uniqueness
- 6 Downloads
Motivated by the notion of a set of uniqueness in a locally compact group G, we introduce and study ideals of uniqueness in the Fourier algebra A(G) of G, and their accompanying operator version, masa-bimodules of uniqueness. We establish a transference between the two notions, and use this result to show that the property of being an ideal of uniqueness is preserved under natural operations.
Unable to display preview. Download preview PDF.
- D. P. Blecher and C. Le Merdy, Operator Algebras and their Modules—an Operator Apace Approach, London Mathematical Society Monographs, Vol. 30, Clarendon Press, Oxford University Press, Oxford, 2004.Google Scholar
- P. Eymard, L’algèbre de Fourier d’un groupe localement compact, Bulletin de la Société Mathématique de France 92 (1964), 181–236.Google Scholar
- C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Grundlehren der Mathematischen Wissenschaften, Vol. 238, Springer-Verlag, New York–Berlin, 1979.Google Scholar
- P. Jolissaint, A characterisation of completely bounded multipliers of Fourier algebras, Colloquium Mathematicum 63 (1992), 311–313.Google Scholar
- A. Ülger, Relatively weak*-closed ideals of A(G), sets of synthesis and sets of uniqueness, Colloquium Mathematicum 136 (2014), 271–296.Google Scholar