Bøger af Vaclav Zizler

One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us the feeling of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems.The main goals of this book are to: introduce the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces; to do so in a manner accessible to graduate students and researchers who have a foundation in Banach space theory; expose the reader to some current avenues of research in biorthogonal systems in Banach spaces; provide notes and exercises related to the topic, as well as suggesting open problems and possible directions of research.The intended audience will have a basic background in functional analysis. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Coverage includes Radon-Nikodym property, finite-dimensional spaces and local theory on tensor products, and more.

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory.