Schauder Bases: Behaviour and Stability

by P.K. Kamthan

(One of the most important and useful tools in functional analysis is the theory of Schauder bases. A meaningful study of this theory comes from consideration of infinite dimensional vector spaces equipped with linear topologies. Broadly, the theory of Schauder bases can be studied with respect to two categories of normed spaces and locally convex spaces. A need has been felt for several years for a book that would cover, in depth, the theory of Schauder bases exclusively in locally convex spaces. The present work deals with the various types of Schauder base, their characterizations and applications. In particular, two important aspects of the theory, similarity and stability, are covered.
The authors aim to stimulate interest in this area in both graduate and advanced undergraduate students. The lucid and systematic treatment of the subject matter will help beginners overcome their initial difficulties. To more advanced workers, the book offers an in-depth treatment of some of the more difficult aspects of the theory, for example, bases and nuclearity of spaces. To experts, this volume offers the advantages of having the theory brought together into a single work of reference.
Containing numerous examples, counter-examples and exercises with solution hints, taken mostly from sequence space theory, the book begins by providing a revision of some essential material. It then proceeds with the elementary aspects of the basic theory and gradually picks up speed to deal with more advanced topics.
The following background knowledge is a first course in functional analysis, including elements on the duality theory of locally convex spaces. Occasionally, for more advanced results, the reader is expected to possess more detailed knowledge of locally convex spaces, although many of the most important results required are summarized in the first chapter)

514 pages, Hardcover

First published July 11, 1988