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

• Autorzy: A. Ülger
• Języki publikacji: EN

Abstrakty

EN

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 $\overline{J(E)}^{w*} = B(G)$).

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 22D15: Group algebras of locally compact groups
• 43A45: Spectral synthesis on groups, semigroups, etc.
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 136
• Numer: 2
• Strony: 271-296

Daty

wydano

2014

Twórcy

autor

A. Ülger

• Department of Mathematics, Koc University, 34450 Sariyer, Istanbul, Turkey

Identyfikatory

DOI

10.4064/cm136-2-9