Banach Spaces and their Applications in Analysis
In recent years there has been a surge of profound new developments in various aspects of analysis by the use of Banach space methods. Many problems, seemingly far from the classical geometry of Banach spaces, have been solved by incorporating Banach space techniques. The book contains papers by participants of the conference “Banach spaces and their applications in analysis” held in May 2006 at Miami University in Oxford, Ohio, in honour of Nigel Kalton's 60th birthday. In this conference, specialists were brought together who have been instrumental in these new developments.
The emphasis of the conference was on applications of Banach spaces in the following areas: nonlinear theory (including Lipschitz classification of Banach and metric spaces and linear programming methods), isomorphic theory of Banach spaces (including connections with combinatorics and set theory), algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces and functional calculus and applications to partial differential equations. The book contains 11 papers by plenary speakers and 16 specialized papers by participants of the conference; the introductory survey of part of the work of N. Kalton is written by G. Godefroy. This article, as well as the rest of the entire volume, illustrates the power of applications of Banach spaces methods and underlying connections between seemingly distant areas of mathematics.