By P. F. X. Müller, W. Schachermayer

This quantity displays the growth made in lots of branches of modern examine in Banach house thought, an analytic method of geometry. together with papers by way of lots of the top figures within the region, it truly is meant to demonstrate the interaction of Banach area idea with harmonic research, chance, advanced functionality idea, and finite dimensional convexity conception. The papers encompass a range of surveys and unique study.

**Read or Download Geometry of Banach Spaces: Proceedings of the Conference Held in Strobl, Austria 1989 PDF**

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L. SHIELDS. Linear functionals on HP spaces 0 < p < 1 J. Reine Angew. Math. 238 (1969), 32-60. M. FLETT. On the rate of growth of mean values of holomorphic and harmonic functions. Proc. London Math. Soc. 20 (1970),749-768. M. FLETT. Lipschizt spaces of functions on the circle and the disc; J. Math. 39 (1972) 125-158. B. GARNETT. " Academic Press. H. E. LITTLEWOOD. Some properties of fractional integrals, II. Math. Z. 34 (1932) 403-439. [K] N. KALTON. Analytic functions in non locally convex spaces and applications.

The research of the first author was supported by NSF-grant DMS 8702329 and the research of the second author was supported by NSF-grant DMS 8901636 1. Introduction, definitions and discussion of results. Although the example given by Enflo in 1973 [5] settled the approximation problem and the basis problem for Banach spaces, a number of closely related problems have continued to arouse interest. If X is a separable Banach space, there are a number of natural properties intermediate between X having the approximation property and having a basis.

Math. Soc. Vol 285, Number 2, October 1984. [Wes] : A. Wessel : Some remarks on Dunford - Pettis operators, strong regularity and the RNP, Seminaire d' analyse Fonctionelle 1985/1986/1987 Paris VI - VII Publications Mathematiques de I1 Universite Paris VII, Paris. R. F. DMS-8807243 26 Ball & Pajor: The entropy of convex bodies with Tew1 extreme points A (rather weak) consequence of a result of Talagrand [T], states that if (xi)^° is a sequence of points in Hilbert space with ||x;|| < , 1 for each i, then, for each n € N, n the convex hull, conv (xi)J° can be covered by 2 (Hilbertian) balls of radius about -4^.