Functional Analysis

Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.

From the reviews of the first edition:

"This is not just a textbook on functional analysis, but on much more . This is certainly a very interesting textbook which can be warmly recommended to students and teachers . The book is well-written, and the reviewer found the motivating first section of each chapter ('Scope of the Chapter') particularly useful, as well as the list of exercises at the end of each chapter." (Jürgen Appell, Zentralblatt MATH, Vol. 1088 (14), 2006)

Klappentext

Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.

Inhalt
I Preliminaries.- II Linear Vector Spaces.- III Introduction to Real Analysis.- IV Topological Spaces.- V Metric Spaces.- VI Normed Spaces.- VII Inner Product Spaces.- VIII Spectral Theory of Linear Operators.- IX Differentiation of Operators.- References.- Index of Symbols.- Name Index.