A Course in Functional Analysis

1. Front Matter

   Pages i-xiv

   PDF

2. Hilbert Spaces

   • John B. Conway

   Pages 1-25

3. Operators on Hilbert Space

   • John B. Conway

   Pages 26-64

4. Banach Spaces

   • John B. Conway

   Pages 65-101

5. Locally Convex Spaces

   • John B. Conway

   Pages 102-126

6. Weak Topologies

   • John B. Conway

   Pages 127-169

7. Linear Operators on a Banach Space

   • John B. Conway

   Pages 170-190

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

   • John B. Conway

   Pages 191-236

9. C*-Algebras

   • John B. Conway

   Pages 237-260

10. Normal Operators on Hilbert Space

    • John B. Conway

    Pages 261-309

11. Unbounded Operators

    • John B. Conway

    Pages 310-352

12. Fredholm Theory

    • John B. Conway

    Pages 353-374

13. Back Matter

    Pages 375-406

    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
• Area
• Banach space
• C*-algebra
• Hilbert space
• banach spaces
• eXist
• functional
• functional analysis
• geometry
• mathematics
• operator
• operator theory
• spectral theory
• topology

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

• Department of Mathematics, Indiana University, Bloomington, USA

  John B. Conway

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