This book introduces the reader to the basic principles of functional analysis theory that are close to nonlinear analysis and topology. The presentation is self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology. Several results are published here for the first time in a monograph. 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. The book is also directed to young researchers in functional analysis and can serve as a reference book, to areas of Banach space.

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:

a [ 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;

a [ to do so in a manner accessible to graduate students and researchers who have a foundation in Banach space theory;

a [ expose the reader to some current avenues of research in biorthogonal systems in Banach spaces;

a [ 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.

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.