Geometric aspects of functional analysis: Israel seminar (GAFA) 1992-94
Joram Lindenstrauss, Vitali D. Milman
Birkhäuser, 1995 - Mathematics - 337 pages
This volume contains a collection of original research papers on recent developments in Banach space theory and related areas by many of the leading research workers in the field. A considerable number of papers are devoted to structure theory of infinite-dimensional Banach spaces. This research ground has experienced a remarkable breakthrough in recent years, which has given new insight into infinite-dimensional geometry (even of Hilbert spaces). Several new results and examples are included in this volume and new research directions are surveyed. Other contributions concern the well established local theory of Banach spaces and its fruitful connection with classical convexity in Rn. The volume also contains several papers on harmonic analysis, probabilistic methods in functional analysis and nonlinear geometry. Research workers and graduate students in Banach space theory, convexity, harmonic analysis and probability will value this book's utility and insight.
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1-unconditional basic sequence 1995 Birkhauser Verlag absolute constant Advances and Applications arbitrary argument assume asymptotic space asymptotic version Banach space Birkhauser Verlag Basel/Switzerland block basis block subspace bounded centrally symmetric consider construction contains convergence convex bodies convex set Corollary defined denote equivalent estimate Euclidean exists follows Fourier series Frechet differentiability Gateaux Gateaux derivatives Geometry Grassmannians hence homeomorphic hyperplane i-th projection implies inequality infinite dimensional subspace integer isotropic position Kolmogorov Lebesgue Lebesgue measure Lemma linear Lipschitz function Lipschitz mapping Math Maurey n-dimensional Banach space n-tuple norm operator orthogonal polytope problem projection class projection functions proof of Theorem Proposition prove Radon transforms result satisfying scalars Schlumprecht spreading model Springer subset subspace game successive blocks Theorem 2.1 Tsirelson spaces unconditional basis uniformly convex unit ball unit vector basis vector game volume winning strategy