Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness

A. Ülger. "Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness." Colloquium Mathematicae 136.2 (2014): 271-296. <http://eudml.org/doc/283950>.

@article{A2014,
abstract = {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 $\overline\{J(E)\}^\{w*\} = B(G)$).},
author = {A. Ülger},
journal = {Colloquium Mathematicae},
keywords = {Fourier algebra; Fourier-Stieltjes algebra; spectral synthesis; set of synthesis; set of uniqueness},
language = {eng},
number = {2},
pages = {271-296},
title = {Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness},
url = {http://eudml.org/doc/283950},
volume = {136},
year = {2014},
}

TY - JOUR
AU - A. Ülger
TI - Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness
JO - Colloquium Mathematicae
PY - 2014
VL - 136
IS - 2
SP - 271
EP - 296
AB - 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 $\overline{J(E)}^{w*} = B(G)$).
LA - eng
KW - Fourier algebra; Fourier-Stieltjes algebra; spectral synthesis; set of synthesis; set of uniqueness
UR - http://eudml.org/doc/283950
ER -