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Edmond E. Granirer, Functional analytic properties of some Banach algebras related to the Fourier algebra

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Volume 1, Issue 3, 1 December 2017, Pages 299-306

 

Abstract. This is a survey of some functional analytic properties of the Banach algebras A_p^r(G)=A_p\cap L^r(G) for locally compact groups G obtained in [18,19, 20, 21]. These include Arens regularity, strict containment for fixed p and increasing r, the RNP and optimisation in A_p^r(G), weak sequential completeness, spectral synthesis, etc. It is found that A_p^r(G) behaves very differently from A_p(G), if r<\infty. The results are new even if G=R or G=Z, the real line or the additive integers.

 

How to Cite this Article:
Edmond E. Granirer, Functional analytic properties of some Banach algebras related to the Fourier algebra, J. Nonlinear Var. Anal. 1 (2017), 299-306.