An Introduction to Banach Space Theory

1. Front Matter

   Pages i-xix

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2. Basic Concepts

   • Robert E. Megginson

   Pages 1-136

3. The Weak and Weak Topologies

   • Robert E. Megginson

   Pages 137-281

4. Linear Operators

   • Robert E. Megginson

   Pages 283-347

5. Schauder Bases

   • Robert E. Megginson

   Pages 349-423

6. Rotundity and Smoothness

   • Robert E. Megginson

   Pages 425-516

7. Back Matter

   Pages 517-599

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Many important reference works in Banach space theory have appeared since Banach's "Théorie des Opérations Linéaires", the impetus for the development of much of the modern theory in this field. While these works are classical starting points for the graduate student wishing to do research in Banach space theory, they can be formidable reading for the student who has just completed a course in measure theory and integration that introduces the L_p spaces and would like to know more about Banach spaces in general. The purpose of this book is to bridge this gap and provide an introduction to the basic theory of Banach spaces and functional analysis. It prepares students for further study of both the classical works and current research. It is accessible to students who understand the basic properties of L_p spaces but have not had a course in functional analysis. The book is sprinkled liberally with examples, historical notes, and references to original sources. Over 450 exercises provide supplementary examples and counterexamples and give students practice in the use of the results developed in the text.

• Banach Space
• Smooth function
• compactness
• differential equation
• functional analysis
• measure

• Mathematics Department, University of Michigan, Ann Arbor, USA

  Robert E. Megginson

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