An Introduction to Hilbert Space (Cambridge Mathematical Textbooks)

Young has done an admirable job at presenting some really beautiful and useful aspects of Hilbert spaces in a manner comprehendable for advanced undergraduates. After reading the book and reflecting on the experience, I'm somewhat amazed at the amount of nice ideas that were presented in such a compact text. The book cannot be compared with more rigorous and comprehensive texts such as Rudin, but you still get all the fundamentals of Hilbert space plus some wonderful applications.I must strongly disagree with the reader from Sao Paolo who says that chapters 12 and 13 are poorly motivated. These chapters are crucial for the final theorem of the book in chapter 16. Parrott's Theorem in chapter 12 is the key to the foundational Nehari's theorem of chapter 15. Chapter 13 explores Hardy spaces which are the setting place for the major theorem of Adamyan, Arov, and Krein in chapter 16. In fact, I found the movement of ideas from chapter 12 to chapter 16 to be marvelously compelling. These chapters have extreme importance for theoretically oriented control engineers.Only a modicum of real and complex analysis is necessary to understand the book. Knowledge of measure theory is not required.

Pretty great intro to functional analysis. It’s not fully rigorous at times (perhaps because its intended audience includes some electrical engineers), but it still gets at the core intuitions on Hilbert spaces that are necessary on a first course. I’d say it’s a really good book to get started, but definitely doesn’t suffice for a deep understanding.

I found this book a concise, well written and accurate introduction to linear algebra. Although some fellow students told me they found it too dry, I had no problem with that.

This book is good to any control engineer who wants to know the background theory of optimization and robust control, but read read an analysis book first.

The writing is very enjoyable to read.The best part of the text is the placement and quality of the exercises. There are short (< 5 minute) exercises that follow the development of key ideas that make the concepts concrete. The end of each chapter also has useful exercises, all of which are good at only drawing upon the content developed in the chapter (rarely need an outside reference to solve exercises).

This book was the required text for a course on Hilbert Spaces at University of Edinburgh that I took back in 1998. This book is very readable, and does a great job of presenting the material. A great read if you plan to study Hilbert Spaces, Banach Spaces, or other topics in Functional Analysis at an introductory level.

The first eleven chapters are an excellent introduction to functional analysis . Both Hilbert and Banach spaces are introduced carefully. Then there are two short chapters on orthogonal expansions and classical fourier series and then linear operators are studied. From the point of view of a person who is interested in applications to physics and engineering one can say that the book is well motivated mainly because is so compact and because of the many notes on applications. Chapters nine , ten and eleven on Green's functions and eigenfunctions expansions are extremely good. Chapters twelve and thirteen are poorly motivated from the point of view of applications.Finally chapters fourteen to sixteen try to exhibit the applications to complex analysis of operator theory and be helpfull to eletrical engineers.I think the book fails in this. So the ten first chapters of the book are excellent . The remaining less so

An unusually readable book on Hilbert space. Very clean notation and very detailed proofs. There are also numerous diagrams. There are also answers to selected problems, but no detailed solutions. If you own one book on Hilbert space, or even functional analysis, this should be it. The author takes great pains to illustrate the ideas involved, not just pound out the theorems.

This book may be a good book but can't judge. It is certainly no introduction. The opening pages jump in to material way over my head, but all I have is one engineering course in Linear Algebra. If you are looking for an Introduction to Hilbert Spaces, this book isn't it. If you are an advanced math student, you may find it better than good. It is brief at least. There are not a lot of illustrations as one reviewer said there were. How one does Analytic Geometry or Functional Analysis without illustrations, I don't know. I give it two stars therefore.

an great book for functional analysis, used for my grad study