Functional analysis 泛函分析 mobi 下载 fb2 夸克云 azw3 网盘 pdf pmlz

This book is meant to serve as an introduction to functional analysis and can be read by anyone with a background in undergraduate mathematics through the junior year. It offers a careful, detailed treatment aimed particularly at advanced undergraduate or beginning graduate mathematics majors as well as to those physics and engineering students who are finding increasing applications of func-tional analysis in their disciplines.

Topics include an introduction to inner product spaces, normed and metric spaces, isometries and completion of a metric space, topological and Banach spaces, equivalent norms and factor spaces, complete orthonormal sets, the Hahn-Banach theorem and its consequences, weak convergence and bounded linear transformations, spectral notions, adjoints and sesquilinear functionals, orthogo-hal projections and positive definite operators, and many other related subjects.Each chapter concludes with exercises intended to test and reinforce the reader's understanding of the material covered.

Prerequisites for optimum comprehension of the text are undergraduate courses in linear algebra and advanced calculus; for the convenience of students, a brief glossary of definitions and notations relevant to linear algebra is included. Proofs of all theorems are as detailed as possible. A helpful bibliography and index of symbols complete this clear and well-written introductory volume.

Preface

CHAPTER 1.Introduction to Inner Product Spaces

CHAPTER 2.Orthogonal Projections and the Spectral Theorem for Normal Transformations

CHAPTER 3.Normed Spaces and Metric Spaces

CHAPTER 4.Isometries and Completion of a Metric Space

CHAPTER 5.Compactness in Metric Spaces

CHAPTER 6.Category and Separable Spaces

CHAPTER 7.Topological Spaces

CHAPTER 8.Banach Spaces,Equivalent Norms,and Factor Spaces

CHAPTER 9.Commutative Convergence,Hilbert Spaces,and Bessel's Inequality

CHAPTER 10.Complete Orthonormal Sets

CHAPTER 11.The Hahn-Bananch Theorem

CHAPTER 12.Consequences of the Hahn-Banach Theorem

CHAPTER 13.The Conjugate Space of (a,b)

CHAPTER 14.Weak Convergence and Bounded Linear Transformations

CHAPTER 15.Convergence in L(X,Y)and the Principle of Uniform Boundedness

CHAPTER 16.Closed Cransformations and the Glosde Graph Theorem

CHAPTER 17.Closures,Conjugate Sransformations,and Complete Contiunity

CHAPTER 18.Spectral Notions

CHAPTER 19.Introduction to Banach Algebras

CHAPTER 20.Adjoints and Sesquilinear Functionals

CHAPTER 21.Some Spectral Results for Normal and Completely Continuous perators

CHAPTER 22.Orthogonal Projections and Positive Definite Operators

CHAPTER 23.Square Roots and a Spectral Decomposition Theorem

CHAPTER 24.Spectral Theorem for Completely Continuous Normal Operators

CHAPTER 25.Spectral Theorem for Bounded,Self-Adjoint Operators

CHAPTER 26.A Second Approach to the Spectral Theorem for Bounded,Self-Adjoint Operators

CHAPTER 27.A Third Approach to the Spectral Theorem for Bounded,Self-Adjoint Operators and Some Consequences

CHAPTER 28.Spectral Theorem for Bounded,Normal Operators

CHAPTER 29.Spectral Theorem for Unbounded,Self-Adjoin Operators

Bibliography

Index of Symbols

Subject Index

Errata

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