A Course in Functional Analysis

1. Front Matter

   Pages i-xvi

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2. Hilbert Spaces

   • John B. Conway

   Pages 1-25

3. Operators on Hilbert Space

   • John B. Conway

   Pages 26-62

4. Banach Spaces

   • John B. Conway

   Pages 63-98

5. Locally Convex Spaces

   • John B. Conway

   Pages 99-123

6. Weak Topologies

   • John B. Conway

   Pages 124-165

7. Linear Operators on a Banach Space

   • John B. Conway

   Pages 166-186

8. Banach Algebras and Spectral Theory for Operators on a Banach Space

   • John B. Conway

   Pages 187-231

9. C*-Algebras

   • John B. Conway

   Pages 232-254

10. Normal Operators on Hilbert Space

    • John B. Conway

    Pages 255-302

11. Unbounded Operators

    • John B. Conway

    Pages 303-346

12. Fredholm Theory

    • John B. Conway

    Pages 347-368

13. Back Matter

    Pages 369-403

    PDF

Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.

• Analysis
• Banach Space
• C*-algebra
• Hilbert space
• calculus
• differential equation
• functional analysis
• measure

Second Edition

J.B. Conway

A Course in Functional Analysis

"This book is an excellent text for a first graduate course in functional analysis . . . Many interesting and important applications are included . . . This book is a fine piece of work. It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author."

—MATHEMATICAL REVIEWS

From the reviews of the second edition:

“This book should be in the library of anyone teaching functional analysis or who wants a working mathematician’s masterfully developed course on functional analysis … . This book is a comprehensive introduction to functional analysis. … I definitely recommend this book to anyone who really want/need to learn true functional analysis for graduate work.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013)

• Department of Mathematics, University of Tennessee, Knoxville, USA

  John B. Conway

    

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