Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. DE ACOSTA. Inequalities for B-valued random vectors with applications to the strong law of large numbers. Ann. Probab. 9 (1981) 157–161.
_____. Stable measures and semi-norms. Ann. Probab. 3 (1975) 365–375.
N. ALON, V. D. MILMAN. Embedding of l k∞ in finite dimensional Banach spaces. Israel J. Math. 45 (1983) 265–280.
D. AMIR, V. D. MILMAN. Unconditional and symmetric sets in n-dimensional normed spaces. Israel J. Math. 37 (1980) 3–20.
_____. A quantitative finite-dimensional Krivine theorem. Israel J. Math. 50 (1985) 1–12.
A. ARAUJO, E. GINÉ. The central limit theorem for real and Banach space valued random variables. Wiley (1980).
Y. BENYAMINI, Y, GORDON. Random factorizations of operators between Banach spaces. J. d'Analyse Jerusalem 39 (1981) 45–74.
A. BEURLING. On analytic extensions of semi-groups of operators. J. Funct. Anal. 6 (1970) 387–400.
C. BORELL. The Brunn-Minkowski inequality in Gauss spaces. Invent. Math. 30 (1975) 207–216.
J. BOURGAIN. New Banach space properties of the disc algebra and H∞. Acta Math. 152 (1984) 1–48.
_____. On martingale transforms on spaces with unconditional and symmetric basis with an appendix on K-convexity constant. Math. Nachrichten (1984).
_____. A complex Banach space such that X and X are not isomorphic. Proc. A.M.S. To appear.
J. BOURGAIN, V. D. MILMAN, H. WOLFSON, On the type of metric spaces. Trans. AMS. To appear.
J. BRETAGNOLLE, D. DACUNHA-CASTELLE, J. L. KRIVINE, Lois stables et espaces L p. Ann. Inst. Henri Poincaré. sect. B. 2 (1966) 231–259.
D. BURKHOLDER. Distribution function inequalities for martingales. Ann. Probab. 1 (1973) 19–42.
A. DVORETZKY. Some results on convex bodies and Banach spaces. Proc. Symp. on Linear Spaces. Jerusalem 1961. p. 123–160.
A. DVORETZKY, C. A. ROGERS. Absolute and unconditional convergence in normed linear spaces. Proc. Nat. Acad. Sci. (USA) 36 (1950) 192–197.
P. ENFLO. Uniform homeomorphisms between Banach spaces-Séminaire Maurey-Schwartz 75–76. Exposé no. 18. Ecole Polytechnique. Paris.
A. EHRHARD. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes Annales E.N.S. 17 (1984) 317–332.
T. FACK. Type and cotype inequalities for non-commutative L p spaces. (Preprint Université Paris 6).
X. FERNIQUE. Intégrabilité des vecteurs gaussiens. C. R. Acad. Sci. Paris A 270 (1970) 1698–1699.
_____. Régularité des trajectoires des fonctions aléatoires gaussiennes. Springer Lecture Notes in Math. no. 480 (1975) 1–96.
T. FIGIEL. On the moduli of convexity and smoothness. Studia Math. 56 (1976) 121–155.
_____. On a recent result of G. Pisier. Longhorn Notes. Univ. of Texas. Functional Analysis Seminar 82/83 p. 1–15.
T. FIGIEL, J. LINDENSTRAUSS, V. D. MILMAN. The dimensions of almost spherical sections of convex bodies. Acta. Math. 139 (1977) 53–94.
T. FIGIEL, N. TOMCZAK-JAEGERMANN. Projections onto Hilbertian subspaces of Banach spaces. Israel J. Math. 33 (1979) 155–171.
D. J. H. GARLING. Convexity smoothness and martingale inequalities. Israel J. Math. 29 (1978) 189–198.
E. D. GLUSKIN. The diameter of the Minkowski compactum is roughly equal to n. Functional Anal. Appl. 15 (1981) 72–73.
E. D. GLUSKIN. Finite dimensional analogues of spaces without a basis. Dokl. Akad. Nauk. SSSR. 261 (1981) 1046–1050 (Russian).
Y. GORDON. On Dvoretzky's theorem and extensions of Slepian's lemma. Lecture no. II Israel Seminar on Geometrical Aspects of Functional Analysis 83–84. Tel Aviv University.
Some inequalities for Gaussian processes and applications. To appear.
J. HOFFMANN-JØRGENSEN. Sums of independent Banach space valued random variables. Aarhus University. Preprint series 1972–73 no. 15.
_____. Sums of independent Banach space valued random variables. Studia Math. 52 (1974) 159–186.
K. ITO, M. NISIO. On the convergence of sums of independent Banach space valued random variables. Osaka J. Math. 5 (1968) 35–48
R. C. JAMES. Non reflexive spaces of type 2. Israel J. Math. 30 (1978) 1–13.
W. B. JOHNSON, G. SCHECHTMAN. Embedding ℓ m p into ℓ n1 . Acta Math. 149 (1982) 71–85.
J. P. KAHANE. Some random series of functions. (1968) Heath Mathematical Monographs. Second Edition, Cambridge University Press (1985).
T. KATÔ. A characterization of holomorphic semi-groups. Proc. Amer. Math. Soc. 25 (1970) 495–498.
H. KÖNIG, L. TZAFRIRI. Some estimates for type and cotype constants. Math. Ann. 256 (1981) 85–94.
J. L. KRIVINE. Sons-espaces de dimension finie des espaces de Banach réticulés. Annals of Maths. 104 (1976) 1–29.
J. KUELBS. Kolmogorov's law of the iterated logarithm for Banach space valued random variables. Illinois J. Math. 21 (1977) 784–800.
S. KWAPIEŃ. Isomorphic characterizations of inner product spaces by orthogonal series with vector coefficients. Studia Math. 44 (1972) 583–595.
H. LANDAU, L. SHEPP. On the supremum of a Gaussian process. Sankhya, A32 (1970) 369–378.
R. LEPAGE, M. WOODROOFE, J. ZINN. Convergence to a stable distribution via order statistics. Ann. Probab. 9 (1981) 624–632.
D. LEWIS. Ellipsoids defined by Banach ideal norms. Mathematika 26 (1979) 18–29.
P. MANKIEWICZ. Finite dimensional Banach spaces with symmetry constant of order √n. Studia Math. To appear.
M. B. MARCUS, G. PISIER. Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes. Acta Math. 152 (1984) 245–301.
B. MAUREY. Type et cotype dans les espaces munis de structure locale inconditionnelle. Séminaire Maurey-Schwartz 73–74. Exposé no. 24–25 Ecole Polytechnique, Paris.
_____. Construction de suites symétriques C.R.A.S. Sci. Paris. A. 288 (1979) 679–681.
B. MAUREY, G. PISIER. Séries de variables aléatoires vectorielles indépendantes et géométrie des espaces de Banach. Studia Math 58 (1976) 45–90.
P. A. MEYER. Note sur les processus d'Ornstein-Uhlenbeck. Séminaire de Probabilités XVI. p. 95–132. Lecture notes in Math no. 920, Springer 1982.
V. D. MILMAN. A new proof of the theorem of A. Dvoretzky on sections of convex bodies. Functional Anal. Appl. 5 (1971) 28–37.
_____. Some remarks about embedding of ℓ k1 in finite dimensional spaces. Israel J. Math. 43 (1982), 129–138.
V. D. MILMAN, G. SCHECHTMAN. Asymptotic theory of finite dimensional normed spaces. Springer Lecture Notes. Vol. 1200.
A. PAJOR. Plongement de ℓ n1 dans les espaces de Banach complexes. C. R. Acad. Sci. Paris A 296 (1983) 741–743.
_____. Thèse de 3e cycle. Université Paris 6. November 84.
G. PISIER, Les inégalités de Khintchine-Kahane d'aprés C. Borell. Exposé no. 7. Séminaire sur la géométrie des espaces de Banach-1977–78. Ecole Polytechnique Palaiseau.
_____. On the dimension of the ℓ n p -subspaces of Banach spaces, for 1<p<2. Trans. A.M.S. 276 (1983) 201–211.
_____. Martingales with values in uniformly convex spaces. Israel J. Math. 20 (1975) 326–350.
_____. Un exemple concernant la super-réflexivité. Annexe no. 2. Séminaire Maurey-Schwartz 1974–75. Ecole Polytechnique. Paris.
_____. Holomorphic semi-groups and the geometry of Banach spaces. Annals of Maths. 115 (1982) 375–392.
_____. Remarques sur les classes de Vapnik-Červonenkis. Ann. Inst. Henri Poincaré, Probabilités et Statistiques, 20 (1984) 287–298.
J. ROSINSKI. Remarks on Banach spaces of stable type. Probability and Math. Statist. 1 (1980) 67–71.
G. SCHECHTMAN. Random embeddings of Euclidean spaces in sequence spaces. Israel J. Math. 40 (1981) 187–192.
_____. Lévy type inequality for a class of finite metric spaces. Martingale Theory in Harmonic Analysis and Banach spaces. Cleveland 1981. Springer Lecture Notes no. 939, p. 211–215.
A. SZANKOWSKI. On Dvoretzky's theorem on almost spherical sections of convex bodies. Israel J. Math. 17 (1974) 325–338.
S. SZAREK. The finite dimensional basis problem with an appendix on nets of Grassman manifolds. Acta Math. 151 (1983) 153–179.
_____. On the existence and uniqueness of complex structure and spaces with few operators. Trans. A.M.S. to appear.
_____. A superreflexive Banach space which does not admit complex structure. To appear.
_____. A Banach space without a basis which has the bounded approximation property. To appear.
N. TOMCZAK-JAEGERMANN. On the moduli of convexity and smoothness and the Rademacher averages of the trace classes S p (1<p<∞). Studia Math. 50 (1974) 163–182.
L. TZAFRIRI. On Banach spaces with unconditional basis. Israel J. Math. 17 (1974) 84–93.
_____. On the type and cotype of Banach spaces. Israel J. Math. 32 (1979) 32–38.
V. YURINSKII. Exponential bounds for large deviations. Theor. Probability Appl. 19 (1974) 154–155.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pisier, G. (1986). Probabilistic methods in the geometry of Banach spaces. In: Letta, G., Pratelli, M. (eds) Probability and Analysis. Lecture Notes in Mathematics, vol 1206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076302
Download citation
DOI: https://doi.org/10.1007/BFb0076302
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16787-7
Online ISBN: 978-3-540-40955-7
eBook Packages: Springer Book Archive