Functional Analysis : : A Terse Introduction / / Humberto Rafeiro, Gerardo Chacón, Juan Camilo Vallejo.

• Superior document: Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017
• VerfasserIn: Chacón, Gerardo,; Rafeiro, Humberto,; Vallejo, Juan Camilo,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2016]; ©2017
• Year of Publication: 2016
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XVIII, 227 p.)

This textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems.The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents:List of FiguresBasic NotationChoice PrinciplesHilbert SpacesCompleteness, Completion and DimensionLinear OperatorsFunctionals and Dual SpacesFourier SeriesFourier TransformFixed Point TheoremBaire Category TheoremUniform Boundedness PrincipleOpen Mapping TheoremClosed Graph TheoremHahn–Banach TheoremThe Adjoint OperatorWeak Topologies and ReflexivityOperators in Hilbert SpacesSpectral Theory of Operators on Hilbert SpacesCompactnessBibliographyIndex

Table of Contents

Frontmatter -- Contents -- List of Figures -- Basic Notation -- 1. Choice Principles -- 2. Hilbert Spaces -- 3. Completeness, Completion and Dimension -- 4. Linear Operators -- 5. Functionals and Dual Spaces -- 6. Fourier Series -- 7. Fourier Transform -- 8. Fixed Point Theorem -- 9. Baire Category Theorem -- 10. Uniform Boundedness Principle -- 11. Open Mapping Theorem -- 12. Closed Graph Theorem -- 13. Hahn–Banach Theorem -- 14. The Adjoint Operator -- 15. Weak Topologies and Reflexivity -- 16. Operators in Hilbert Spaces -- 17. Spectral Theory of Operators on Hilbert Spaces -- 18. Compactness -- Bibliography -- Index