Handbook of the Geometry of Banach Spaces (Volume 2)

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, 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.The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter 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. Most have an extensive bibliography. 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.As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory. Handbook of the Geometry of Banach Spaces presents 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. contains all the background needed for reading any other chapter. Each of the articles after this 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.As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory. books_005......Page 1 books_004......Page 2 books_003......Page 3 books_002......Page 4 1......Page 5 2......Page 7 3......Page 8 4......Page 71 5......Page 98 6......Page 130 7......Page 175 8......Page 199 9......Page 245 10......Page 296 11......Page 330 12......Page 358 13......Page 421 14......Page 455 15......Page 514 16......Page 542 17......Page 598 18......Page 630 19......Page 665 20......Page 697 21......Page 736 22......Page 810 23......Page 812 24......Page 814 25......Page 815 26......Page 816 27......Page 840 Encouraged by new perspectives in Banach space theory, the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications. The goal of this chapter is to reveal the power of descriptive set theory in penetrating the structure of Banach spaces.