Weakly amenable groups and the RNP for some Banach algebras related to the Fourier algebra

• Autorzy: Edmond E. Granirer
• Języki publikacji: EN

Abstrakty

EN

It is shown that if G is a weakly amenable unimodular group then the Banach algebra $A_{p}^r(G) = A_{p} ∩ L^r(G)$, where $A_{p}(G)$ is the Figà-Talamanca-Herz Banach algebra of G, is a dual Banach space with the Radon-Nikodym property if 1 ≤ r ≤ max(p,p'). This does not hold if p = 2 and r > 2.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 46J20: Ideals, maximal ideals, boundaries
• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 43A80: Analysis on other specific Lie groups
• 46J10: Banach algebras of continuous functions, function algebras
• 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
• 22E30: Analysis on real and complex Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 130
• Numer: 1
• Strony: 19-26

Daty

wydano

2013

Twórcy

autor

Edmond E. Granirer

• Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada

Identyfikatory

DOI

10.4064/cm130-1-2