Some remarks on Q-algebras
Varopoulos, Nicolas Th.
Annales de l'Institut Fourier, Tome 22 (1972), p. 1-11 / Harvested from Numdam
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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 ℓ p , (1≤p≤∞) appartiennent à cette classe et que A n =ℨL 1 (Z;1+|n| α ) appartient à cette classe si et seulement si α>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 ℓ p , (1≤p≤∞) are Q algebras and that A n =ℨL 1 (Z;1+|n| α ) is a Q-algebra if and only if α>1/2.

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     author = {Varopoulos, Nicolas Th.},
     title = {Some remarks on $Q$-algebras},
     journal = {Annales de l'Institut Fourier},
     volume = {22},
     year = {1972},
     pages = {1-11},
     doi = {10.5802/aif.432},
     mrnumber = {49 \#3544},
     zbl = {0235.46074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1972__22_4_1_0}
}

Varopoulos, Nicolas Th. Some remarks on $Q$-algebras. Annales de l'Institut Fourier, Tome 22 (1972) pp. 1-11. doi : 10.5802/aif.432. http://gdmltest.u-ga.fr/item/AIF_1972__22_4_1_0/

[1] J. Wermer, Quotient algebras of uniform algebras, Symposium on Function algebras and rational approximation, University of Michigan 1969.

[2] A. M. Davie, Quotient algebras of uniform algebras (to appear). | Zbl 0264.46055

[3] L. Schwartz, Séminaire 1953-1954, Produits tensoriels topologiques, Exposé n° 7 II.

[4] A. P. Calderon, Intermediate spaces and interpolation, the complex method. Studia Math., T. xxiv (1964), 113-190. | MR 29 #5097 | Zbl 0204.13703

[5] N. Th. Varopoulos, Tensor algebras and harmonic analysis, Acta Math. 119 (1967), 51-111. | MR 39 #1911 | Zbl 0163.37002

[6] A. Zygmund, Trigonometric series, C.I.P. (1959), vol. I, ch. VI, § 3 ; vol. II, ch. XII § 8. | Zbl 0085.05601

[7] N. Th. Varopoulos, Sur les quotients des algèbres uniformes, C.R. Acad. Sci. t. 274 (A) p. 1344-1346. | Zbl 0245.46072

[8] N. Th. Varopoulos, Tensor algebras over discrete spaces, J. Functional Analysis, 3 (1969), 321-335. | MR 40 #3328 | Zbl 0183.14502