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Exercises in functional analysis / by Constantin Costara and Dumitru Popa.

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Author/Creator:
Costara, Constantin.
Language:
English.
Publication date:
2003
Imprint:
Dordrecht ; Boston : Kluwer Academic Publishers, c2003.
Format:
  • Book
  • x, 451 p. ; 25 cm.
Bibliography:
Includes bibliographical references (p. [444]-446) and index.
Contents:
  • Some Standard Notations and Conventions
  • Part I. Normed spaces
  • Chapter 1.. Open, closed, and bounded sets in normed spaces
  • 1.1. Exercises
  • 1.2. Solutions
  • Chapter 2.. Linear and continuous operators on normed spaces
  • 2.1. Exercises
  • 2.2. Solutions
  • Chapter 3.. Linear and continuous functionals. Reflexive spaces
  • 3.1. Exercises
  • 3.2. Solutions
  • Chapter 4.. The distance between sets in Banach spaces
  • 4.1. Exercises
  • 4.2. Solutions
  • Chapter 5.. Compactness in Banach spaces. Compact operators
  • 5.1. Exercises
  • 5.2. Solutions
  • Chapter 6.. The Uniform Boundedness Principle
  • 6.1. Exercises
  • 6.2. Solutions
  • Chapter 7.. The Hahn-Banach theorem
  • 7.1. Exercises
  • 7.2. Solutions
  • Chapter 8.. Applications for the Hahn-Banach theorem
  • 8.1. Exercises
  • 8.2. Solutions
  • Chapter 9.. Baire's category. The open mapping and closed graph theorems
  • 9.1. Exercises
  • 9.2. Solutions
  • Part II. Hilbert spaces
  • Chapter 10.. Hilbert spaces, general theory
  • 10.1. Exercises
  • 10.2. Solutions
  • Chapter 11.. The projection in Hilbert spaces
  • 11.1. Exercises
  • 11.2. Solutions
  • Chapter 12.. Linear and continuous operators on Hilbert spaces
  • 12.1. Exercises
  • 12.2. Solutions
  • Part III. General topological spaces
  • Chapter 13.. Linear topological and locally convex spaces
  • 13.1. Exercises
  • 13.2. Solutions
  • Chapter 14.. The weak topologies
  • 14.1. Exercises
  • 14.2. Solutions.
Summary:
This book of exercises in functional analysis contains almost 450 exercises (all with complete solutions), providing supplementary examples, counter-examples and applications for the basic notions usually presented in an introductory course in functional analysis.
Contributor:
Popa, Dumitru.
Series:
Kluwer texts in the mathematical sciences ; v. 26.
Subjects:
ISBN:
1402015607
9781402015601

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