A Concise Introduction to Functional Analysis

1. Auflage 2025
ISBN: 978-1-041-10328-8
Verlag: CRC Press

Buch, Englisch, 240 Seiten, Format (B × H): 178 mm x 254 mm

A Concise Introduction to Functional Analysis is designed to serve a one-semester introductory graduate (or advanced undergraduate) course in functional analysis.

The text is pragmatically structured so that each unit corresponds to one class, with the hope of being helpful for both students and teachers. It is expected that this text will provide students with a strong general understanding of the subject, and that they should feel well equipped to take on the more advanced texts and courses covering topics not treated here.

Features

· Numerous examples and counterexamples to illustrate such abstract concepts

· Over 430 exercises, with partial solutions included in the book itself

· Minimal pre-requisites beyond linear algebra and general topology.

Zielgruppe

Postgraduate and Undergraduate Advanced

Autoren/Hrsg.

Oliveira

Oliveira, C´esar R. de

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Preface Selected Notation Chapter 1 Normed Spaces Chapter 2 Compactness and Completion Chapter 3 Separable Spaces. Linear Operators Chapter 4 Bounded Operators and Dual Spaces Chapter 5 Banach Fixed Point Chapter 6 Baire Theorem Chapter 7 Uniform Boundedness Principle Chapter 8 Open Mapping Theorem Chapter 9 Closed Graph Theorem Chapter 10 Hahn-Banach Theorem Chapter 11 Proof of Hahn-Banach Chapter 12 Applications of Hahn-Banach Theorem Chapter 13 Adjoint Operators in N Chapter 14 Weak Convergence Chapter 15 Weak Topologies Chapter 16 Reflexive Spaces and Compactness Chapter 17 Hilbert Spaces Chapter 18 Orthogonal Projection Chapter 19 Riesz Representation in H Chapter 20 Self-Adjoint Operators Chapter 21 Orthonormal Bases Chapter 22 Fourier Series Chapter 23 Operations on Banach Spaces Chapter 24 Compact Operators Chapter 25 Compact Operators on H Chapter 26 Hilbert-Schmidt Operators Chapter 27 The Spectrum Chapter 28 Spectral Classification Chapter 29 Spectra of Self-Adjoint Operators Chapter 30 Spectra of Compact Operators Solutions to Selected Exercises Bibliography Index

Über Autor(innen)

César R. de Oliveira earned his Ph.D. in Physics from the University of São Paulo in 1987. He has been a visiting professor at the Università degli Studi di Milano (1991–1992) and the University of British Columbia (2008–2009). He is currently a Full Professor at the Federal University of São Carlos, in the Department of Mathematics.

His research lies in the field of Mathematical Physics, with publications in both mathematics and physics journals. He has supervised twelve Ph.D. students, and his main areas of interest include Schrödinger and Dirac operators, the Aharonov–Bohm effect, mathematical models of graphene, quantum (in)stability, and dynamical localization.

He also enjoys writing textbooks and has authored four of them. In 2000, he published an introductory mechanics book (in Portuguese, with animations and interactive content on CD-ROM) through his University. In 2010, he released a graduate-level book on functional analysis (in Portuguese) with IMPA (Rio de Janeiro). In 2009, the book Spectral Theory and Quantum Dynamics was published by Birkhäuser (Switzerland). Most recently, in 2023, he co-authored Spectral Measures and Dynamics: Typical Behaviors with M. Aloisio and S. Carvalho.