Bochner property in Banach spaces
Annales de l'I.H.P. Probabilités et statistiques (1981)
- Volume: 17, Issue: 1, page 1-19
- ISSN: 0246-0203
Access Full Article
topHow to cite
topNaik-Nimbalkar, Uttara. "Bochner property in Banach spaces." Annales de l'I.H.P. Probabilités et statistiques 17.1 (1981): 1-19. <http://eudml.org/doc/77153>.
@article{Naik1981,
author = {Naik-Nimbalkar, Uttara},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {positive definite function; characteristic function; Bochner's theorem; Bochner property; cotype 2},
language = {eng},
number = {1},
pages = {1-19},
publisher = {Gauthier-Villars},
title = {Bochner property in Banach spaces},
url = {http://eudml.org/doc/77153},
volume = {17},
year = {1981},
}
TY - JOUR
AU - Naik-Nimbalkar, Uttara
TI - Bochner property in Banach spaces
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1981
PB - Gauthier-Villars
VL - 17
IS - 1
SP - 1
EP - 19
LA - eng
KW - positive definite function; characteristic function; Bochner's theorem; Bochner property; cotype 2
UR - http://eudml.org/doc/77153
ER -
References
top- [1] A. De Acosta, Existence and convergence of probability measures in Banach . spaces, Trans. Amer. Math. Soc., t. 152, 1970, p. 273-298. Zbl0226.60007MR267614
- [2] A. De Acosta, Banach spaces of stable type and the generation of stable measures, prepint, 1975.
- [3] A. Badrikian, Séminaire sur les fonctions aléatoires linéaires et les measures cylindriques, Lecture Notes in Math. (Springer-Verlag), t. 139, 1970. Zbl0209.48402MR279271
- [4] P. Billingsley, Convergence of probability measures, Wiley, New York, MR, t. 38, p. 1718. Zbl0172.21201MR1700749
- [5] L. Breiman, Probability, Addison-Wesley, Reading, 1968. Zbl0174.48801MR229267
- [6] N. Dunford and J.T. Schwartz, Linear operators, Interscience, New York, t. 1, 1957. Zbl0084.10402
- [7] W. Feller, An introduction to probability theory and its applications, Vol. II, John Wiley and Sons, New York, 1966. Zbl0138.10207MR210154
- [8] X. Fernique, Integrabilite des vecteurs Gaussien, G. R. Acad. Sc. Paris, Sene A. t. 270, 1971, p. 1698-1699. Zbl0206.19002MR266263
- [9] D.J.H. Garling, Functional central limit theorem in Banach spaces, Ann. Prob., t. 4, 1976, p. 600-611. Zbl0343.60014MR423449
- [10] L. Gross, Harmonic analysis on Hilbert spaces, Mem. Amer. Math. Soc., t. 46, 1963. Zbl0118.32201MR161095
- [11] P. Halmos, Measure theory, Princeton, 1950. Zbl0040.16802MR33869
- [12] K. Ito and M. Nisio, Sums of independent Banach space valued random variables. Osaka, J. Math., t. 5, 1968, p. 35-48. Zbl0177.45102MR235593
- [13] J. Kuelbs, Fourier Analysis on linear metric spaces, Trans. Amer. Math. Soc., t. 181, 1973, p. 293-311. Zbl0291.60001MR331455
- [14] S. Kwapien, Isomorphic characterizations of inner-product spaces by orthogonal series with vector valued coefficients, Studia Math., t. 44, 1972, p. 583-595. Zbl0256.46024MR341039
- [15] J. Lindenstrauss and A. Pelczynski, Absolutely summing operators in Lp-spaces and their applications, Studia Math., t. 29, 1968, p. 275-326. Zbl0183.40501MR231188
- [16] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., t. 338, 1973, Springer-Verlag, New York. Zbl0259.46011MR415253
- [17] M. Loeve, Probability theory, 3rd Ed., Van Nostrand, Princeton, 1963. Zbl0108.14202MR203748
- [18] V. Mandrekar, On Bochner and Levy theorems in Orlicz spaces, Symp. Math., t. 21, 1977, p. 177-186. Zbl0372.46033MR482904
- [19] V. Mandreakar, Characterization of Banach space through validity of Bochner Theorem, Lecture Notes in Math., t. 644, 1977, Springer-Verlag. Zbl0498.60010
- [20] B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp, SociétéMathématique de France, Astérique, t. 11, 1974, p. 1-163. Zbl0278.46028MR344931
- [21] B. Maurey and G. Pisier, Series de variables aleatones vectorielles independentes et proprietes geometriques des espaces de Banach, Studia Math., t. 58, 1976, p. 45-90. Zbl0344.47014MR443015
- [22] D.K.H. Mustari, Certain general questions in the theory of probability measures in linear spaces, Theor. Prob. Appl. (S. I. A. M. translations), t. 18, 1973, p. 64-75. Zbl0304.60003
- [23] D.K.H. Mustari, On a probabilistic characterization of Hilbert space, Theor. Prob. Appl. (S. I. A. M. translation), t. 21, 1976, p. 410-412. Zbl0358.60008MR418178
- [24] K.R. Parthasarathy, Propability measures on metric spaces, Academic Press, New York, 1967. Zbl0153.19101MR226684
- [25] V. Yu Prohorov, Convergence of random processes and limit theorems in probability theory, Theor. Prob. Appl. (S. I. A. M. translation), t. 1, 1956, p. 157-214. Zbl0075.29001MR84896
- [26] H. Rosenthal, The Banach spaces C(K) and Lp(μ). Bull. Amer. Math. Soc., t. 81, no. 5, 1975, p. 763-781. Zbl0334.46033MR380381
- [27] H. Sato, Hilbertian support of probability measures on a Banach space, Lecture Notes in Math., t. 709, Springer Verlag. Zbl0398.60006
- [28] V. Sazanov, On characteristic functionals, Theor. Prob. Appl. (S. I. A. M. translation), t. 3, 1958, p. 189-193. Zbl0089.33801
- [29] Michael Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist., t. 41, 1970, 412-421. Zbl0196.19401MR254915
- [30] A. Tortrat, Sur les lois e(λ) dans les espaces vectoriels, Applications aux lois stables, preprint, Lab. de Prob., Univ. of Paris, 1975.
- [31] B. Maurey, Un théorème de prolongement, C. R. A. S., t. 279, 1974, p. 329-332. Zbl0291.47001MR355539
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.