My chosen book for Functional Analysis is the one by Joseph Muscat (Muscat 2024) - I am using the second edition. The author has his own book page.
Why this book? There are many books that could be chosen: I have worked through others in previous years, in particular (Kreyszig 1991) and (Maddox 1988). However, partly because of its breadth, partly because of a personal connection, and partly because of it being a recent publication, I picked Muscat’s book when restarting my study of this subject.
The book is divided into three parts, starting with Metric Spaces, continuing with Banach and Hilbert Spaces, and concluding with Banach Algebras. Wrapped in are introductions to some real analysis, complex analysis and measure theory.
This and succeeding posts list some additional resources I’ve used while working through the book - there’s nothing special about these, other than that I found them useful additional material. Other posts will probably appear, focussing on individual parts.
Part I: Metric Spaces
Video courses:
- Introduction to Metric Spaces by Paige Bright - MIT OCW.
- A2 Metric Spaces by Prof. Ben Green - Oxford University.
- Functional Analysis by Dr. Joel Feinstein - University of Nottingham. These videos cover a complete course, from Metric Spaces to Banach Algebras, but with less detail than the book, so this series makes a useful introduction.