Some remarks on $Q$-algebras

Varopoulos, Nicolas Th.

Annales de l'Institut Fourier, Tome 22 (1972) no. 4, pp. 1-11.

On fait une étude des algèbres qui sont des quotients des algèbres uniformes et on démontre que cette classe est stable par interpolation. On démontre en particulier que le ${\ell }^p$, $(1\le p\le \infty )$ appartiennent à cette classe et que $A_n=ℨL^1(\mathbf{Z};1+|n{|}^{\alpha })$ appartient à cette classe si et seulement si $\alpha >1/2$.

We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that ${\ell }^p$, $(1\le p\le \infty )$ are $Q$ algebras and that $A_n=ℨL^1(\mathbf{Z};1+|n{|}^{\alpha })$ is a $Q$-algebra if and only if $\alpha >1/2$.

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