Linear Functional Analysis for Scientists and Engineers

"A textbook designed for an initial but sophisticated study of a classical compulsory course in the modern mathematical education ... . a significant part of the book is devoted to examples illustrating the concepts introduced and the results proved earlier. Each chapter (except the first) ends with 40 well-selected and interesting exercises which essentially complement the main text. At the end of the book, solutions to all these exercises are given. In conclusion, the book is interesting and useful. The simplicity and clarity in the presentation of basic ideas and results, the absence of cumbersome arguments, and a good set of exercises make the book easily readable and valuable to all mathematicians: students, teachers and researchers." (Prof. Petr P. Zabreiko, Belarussian State University at Minsk, Belarus)

Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance structure of a metric space, functional analysis is increasingly gaining the attention of not only mathematicians but also scientists and engineers.This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance structure of a metric space, functional analysis is increasingly gaining the attention of not only mathematicians but also scientists and engineers. The purpose of the text is to present the basic aspects of functional analysis to this varied audience, keeping in mind the considerations of applicability. A novelty of this book is the inclusion of a result by Zabreiko, which states that every countably subadditive seminorm on a Banach space is continuous. Several major theorems in functional analysis are easy consequences of this result.
The entire book can be used as a textbook for an introductory course in functional analysis without having to make any specific selection from the topics presented here. Basic notions in the setting of a metric space are defined interms of sequences. These include total boundedness, compactness, continuity and uniform continuity. Offering concise and to-the-point treatment of each topic in the framework of a normed space and of an inner product space, the book represents a valuable resource for advanced undergraduate students in mathematics, and will also appeal to graduate students and faculty in the natural sciences and engineering. The book is accessible to anyone who is familiar with linear algebra and real analysis.