A Course in Functional Analysis

Rating:
Summary: A Course in Functional Analysis ... the title is correct!
Review: I learned functional analysis by studying this book. I did this under the direction of a master teacher, John Erdman, who taught via a modified Moore Method. I found this very inspirational and challenging. BEFORE I took the course, I did not enjoy browsing the book, BUT I learned that the book, upon combination with the right amount of focus and effort, did a remarkable job of bringing functional analysis alive ... of transmiting the real essence to young, "sprouting" mathematicians. There is also an informality that brings a freshness to the book ... and this in a subject that could easily be studied without encountering this important ingredient in a mathematician's training.

This book has as it's high point and goal the spectral theorem for normal operators. I add this because no one book can be all encompassing. If this and the spectral theorem goal are kept in mind, the omissions and emphasis found in the book will be found to be completely natural.

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 (with an eye to the spectral theorem for normal operators).

Rating:
Summary: An Excellent Book !
Review: This book is just excellent. The author decides to do something a little unusual, and starts talking about "Hilbert Spaces" before talking about "Banach Spaces". Conway writes down the matereal in a great way. He gives proves to almost every proposition, and gives lots of EXAMPLES and EXCERCISES (which are not given in most of the books about this subject). It's a good book for people who have never read this book before, as well as people who are currently studying the course. Also, conway extends the book's content by writing about advanced subjects (that are not studied in a first course about the subject), like locally convex spaces, weak topologies and even unbounded operators.

Rating:
Summary: An Excellent Book !
Review: This book is just excellent. The author decides to do something a little unusual, and starts talking about "Hilbert Spaces" before talking about "Banach Spaces". Conway writes down the matereal in a great way. He gives proves to almost every proposition, and gives lots of EXAMPLES and EXCERCISES (which are not given in most of the books about this subject). It's a good book for people who have never read this book before, as well as people who are currently studying the course. Also, conway extends the book's content by writing about advanced subjects (that are not studied in a first course about the subject), like locally convex spaces, weak topologies and even unbounded operators.