Introduction to Banach Spaces, I

This volume consists of a collection of articles from experts with a rich research and educational experience. The contributors of this volume are: Y Benyamini, M Gonzalez, V Muller, S Reich, E Matouskova, A J Zaslavski and A R Palacios.

"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.

This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. <P>The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained.