no. 4
Some remarks on Q-algebras
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 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.

@article{AIF_1972__22_4_1_0,
     author = {Varopoulos, Nicolas Th.},
     title = {Some remarks on $Q$-algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {1--11},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {22},
     number = {4},
     year = {1972},
     doi = {10.5802/aif.432},
     zbl = {0235.46074},
     mrnumber = {49 #3544},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.432/}
}
TY  - JOUR
AU  - Varopoulos, Nicolas Th.
TI  - Some remarks on $Q$-algebras
JO  - Annales de l'Institut Fourier
PY  - 1972
SP  - 1
EP  - 11
VL  - 22
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.432/
DO  - 10.5802/aif.432
LA  - en
ID  - AIF_1972__22_4_1_0
ER  - 
%0 Journal Article
%A Varopoulos, Nicolas Th.
%T Some remarks on $Q$-algebras
%J Annales de l'Institut Fourier
%D 1972
%P 1-11
%V 22
%N 4
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.432/
%R 10.5802/aif.432
%G en
%F AIF_1972__22_4_1_0
Varopoulos, Nicolas Th. Some remarks on $Q$-algebras. Annales de l'Institut Fourier, Tome 22 (1972) no. 4, pp. 1-11. doi : 10.5802/aif.432. https://aif.centre-mersenne.org/articles/10.5802/aif.432/

[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

[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 | Zbl

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

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

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

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

Cité par Sources :