PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1996 | 118 | 3 | 231-243
Tytuł artykułu

On the type constants with respect to systems of characters of a compact abelian group

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that there exists an absolute constant c such that for any positive integer n and any system Φ of $2^n$ characters of a compact abelian group, $2^{-n/2} t_Φ(T) ≤ c n^{-1/2} t_n(T)$, where T is an arbitrary operator between Banach spaces, $t_Φ(T)$ is the type norm of T with respect to Φ and $t_n(T)$ is the usual Rademacher type-2 norm computed with n vectors. For the system of the first $2^n$ Walsh functions this is even true with c=1. This result combined with known properties of such type norms provides easy access to quantitative versions of the fact that a nontrivial type of a Banach space implies finite cotype and nontrivial type with respect to the Walsh system or the trigonometric system.
Słowa kluczowe
Czasopismo
Rocznik
Tom
118
Numer
3
Strony
231-243
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-07-24
poprawiono
1995-11-09
Twórcy
Bibliografia
  • [1] B. Beauzamy, Introduction to Banach Spaces and their Geometry, Notas di Mat. 68, North-Holland, Amsterdam, 1982.
  • [2] J. Bourgain, On trigonometric series in superreflexive spaces, J. London Math. Soc. (2) 24 (1981), 165-174.
  • [3] J. Bourgain, A Hausdorff-Young inequality for B-convex Banach spaces, Pacific J. Math. 101 (1982), 255-262.
  • [4] J. Bourgain, Subspaces of $L_N^∞$, arithmetical diameter and Sidon sets, in: Probability in Banach Spaces V, Proceedings, Medford 1984, Lecture Notes in Math. 1153, Springer, Berlin, 1986, 96-127.
  • [5] J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge Stud. Adv. Math. 43, Cambridge Univ. Press, 1995.
  • [6] H. König and L. Tzafriri, Some estimates for type and cotype constants, Math. Ann. 256 (1981), 85-94.
  • [7] J. L. Krivine, Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. 104 (1976), 1-29.
  • [8] V. Mascioni, On weak cotype and weak type in Banach spaces, Note Mat. 8 (1988), 67-110.
  • [9] B. Maurey et G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), 45-90.
  • [10] V. D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Lecture Notes in Math. 1200, Springer, Berlin, 1986.
  • [11] A. Pietsch, Gradations of the Hilbertian operator norm and geometry of Banach spaces, Forschungsergebnisse Univ. Jena N/89/6.
  • [12] A. Pietsch, Sequences of ideal norms, Note Mat. 10 (1990), 411-441.
  • [13] A. Pietsch and J. Wenzel, Orthonormal systems and Banach space geometry, in preparation.
  • [14] G. Pisier, Sur les espaces de Banach qui ne contiennent pas uniformément de $l_1^n$, C. R. Acad. Sci. Paris Sér. A 277 (1973), 991-994.
  • [15] G. Pisier, Les inégalités de Kahane-Khintchin d'après C. Borell, Séminaire sur la Géometrie des Espaces de Banach (1977-1978), Exposé No. VII, École Polytechnique, Palaiseau.
  • [16] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Ser. in Math. 60, Amer. Math. Soc., Providence, 1986.
  • [17] G. Pisier, Sur les espaces de Banach de dimension finie à distance extrémale d'un espace euclidien, d'après V. D. Milman et H. Wolfson, Séminaire d'Analyse Fonctionnelle (1978-1979), Exposé No. XVI, École Polytechnique, Palaiseau.
  • [18] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Longman, 1988.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv118i3p231bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.