Introduction to functional analysis / Geraldo Botelho, Daniel Pellegrino, Eduardo Teixeira.

Format:

Book

Author/Creator:

Botelho, Geraldo, author.

Pellegrino, Daniel M., author.

Teixeira, Eduardo, author.

Series:

Universitext

Universitext, 0172-5939

Standardized Title:

Fundamentos de análise funcional. English

Language:

English

Portuguese

Subjects (All):

Functional analysis.

Physical Description:

xiii, 340 pages : illustrations ; 24 cm.

Production:

Cham, Switzerland : Springer, [2025]

Language Note:

Translated from the 3rd Brazilian Portugese edition (Rio de Janeiro : Sociedade Brasileira de Matemática, 2023).

Summary:

"This textbook offers an accessible introduction to Functional Analysis, providing a solid foundation for students new to the field. It is designed to support learners with no prior background in the subject and serves as an effective guide for introductory courses, suitable for students in mathematics and other STEM disciplines. The book provides a comprehensive introduction to the essential topics of Functional Analysis across the first seven chapters, with a particular emphasis on normed vector spaces, Banach spaces, and continuous linear operators. It examines the parallels and distinctions between Functional Analysis and Linear Algebra, highlighting the crucial role of continuity in infinite-dimensional spaces and its implications for complex mathematical problems. Later chapters broaden the scope, including advanced topics such as topological vector spaces, techniques in Nonlinear Analysis, and key theorems in theory of Banach spaces. Exercises throughout the book reinforce understanding and allow readers to test their grasp of the material. Designed for students in mathematics and other STEM disciplines, as well as researchers seeking a thorough introduction to Functional Analysis, this book takes a clear and accessible approach. Prerequisites include a strong foundation in analysis in the real line, linear algebra, and basic topology, with helpful references provided for additional consultation"--Back cover.

Contents:

Contents

Preface

Normed Vector Spaces

Continuous Linear Operators

Hahn-Banach Theorems

Duality and Reflexive Spaces

Hilbert Spaces

Weak Topologies

Spectral Theories of Compact Self-Adjoint Operators

Topological Vector Spaces

Introduction to Nonlinear Analysis

Elements of Banach Space Theory

A Zorns Lemma

B Concepts of General Topology

C Measure and Integration

D Answers/hints for selected exercises

Bibliography

Index.

Notes:

Includes bibliographical references (pages 333-335) and index.

ISBN:

3031817907

9783031817908

OCLC:

1476080593