Presenting an overview of most aspects of modern Banach space theory and its applications, this handbook offers up-to-date surveys by a range of expert authors. The surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory and partial differential equations. It begins with a chapter on basic concepts in Banach space theory, which contains all the background needed for reading any other chapter. Each of the 21 articles after his is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods and open problems in its specific direction. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. The handbook should be useful to researchers in Banach theory, as well as graduate students and mathematicians who want to get an idea of the various developments in Banach space theory.
- Limba : Engleza
- Cuprins : Preface. Descriptive Set Theory and Banach Spaces (S.A. Argyros, G. Godefroy, H.P. Rosenthal). Ramsey Methods in Banach Spaces (W.T. Gowers). Quasi-Banach Spaces (N. Kalton). Interpolation of Banach Spaces (N. Kalton, S. Montgomery-Smith). Probabilistic Limit Theorems in the Setting of Banach Spaces (M. Ledoux, J. Zinn). Quotients of Finite-Dimensional Banach Spaces; Random Phenomena (P. Mankiewicz, N. Tomczak-Jaegermann). Banach Spaces with few Operators (B. Maurey). Type-cotype and K-convexity (B. Maurey). Distortion and Asymptotic Structure (E. Odell, T. Schlumprecht). Sobolev Spaces (A. Pelczynski, M. Wojciechowski). Operator Spaces (G. Pisier). Non-commutative Lp-spaces (G. Pisier, Q. Xu). Geometric Measure Theory in Banach Spaces (D. Preiss). The Banach Spaces C (K). Concentration, Results and Applications (G. Schechtman). Uniqueness of Structure in Banach Spaces (L. Tzafriri). Spaces of Analytic Functions with Integral Norm (P. Wojtaszczyk). Extension of Bounded Linear Operators (M. Z
- Data Publicarii : 06 May 2003
- Format : Hardback
- Numar pagini : 870
- ISBN : 9780444513052