On the dichotomy problem for tensor algebras
HTML articles powered by AMS MathViewer
- by J. Bourgain PDF
- Trans. Amer. Math. Soc. 293 (1986), 793-798 Request permission
Abstract:
Let $I$, $J$ be discrete spaces and $E \subset I \times J$. Then either $E$ is a $V$-Sidon set (in the sense of $[{\mathbf {2}},\S 11]$), or the restriction algebra $A(E)$ is analytic. The proof is based on probabilistic methods, involving Slépian’s lemma.References
- Jean Bourgain and Vitali Milman, Dichotomie du cotype pour les espaces invariants, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 9, 263–266 (French, with English summary). MR 785065 G. Graham and C. McGehee, Essays in commutative harmonic analysis, Springer, New York, 1982.
- X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, École d’Été de Probabilités de Saint-Flour, IV-1974, Lecture Notes in Math., Vol. 480, Springer, Berlin, 1975, pp. 1–96 (French). MR 0413238
- S. Kwapień and A. Pełczyński, Absolutely summing operators and translation-invariant spaces of functions on compact abelian groups, Math. Nachr. 94 (1980), 303–340. MR 582532, DOI 10.1002/mana.19800940118
- Yitzhak Katznelson and Paul Malliavin, Un critère d’analyticité pour les algĕres de restriction, C. R. Acad. Sci. Paris 261 (1965), 4964–4967 (French). MR 203373 —, Verification statistique de la conjecture de la dichotomie sur une classe d’algèbres de restriction, C. R. Acad. Sci. Paris Sér. A—B 262 (1966), A490-A492.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 293 (1986), 793-798
- MSC: Primary 43A25; Secondary 42A16, 43A46
- DOI: https://doi.org/10.1090/S0002-9947-1986-0816324-7
- MathSciNet review: 816324