Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are σ(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C₀(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to the above issues, we present a series of results about closed sets of uniqueness (i.e. closed sets E for which ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-9,
author = {A. \"Ulger},
title = {Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {271-296},
zbl = {1306.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-9}
}
A. Ülger. Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness. Colloquium Mathematicae, Tome 135 (2014) pp. 271-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-9/