Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) 1st Edition

This book is firstly a presentation of the basic theory of functional analysis in a very clear way from the point of view of the logical structures being presented. Lax's writing is clear and to-the-point. (although there is the occasional typographical/ grammatical error, they are easily overlooked.) The chapters are bite-size (~10 pages each) and alternate between theoretical explorations and complementary illustrations with examples. Lax includes all the usual material from a First Course in Functional Analysis, and enough other material for a second course on operator theory, and a third on Topics in Functional Analysis and Partial Differential Equations. In part Lax succeeds in providing such a dense coverage of a broad body of material by relying in part on the reader's familiarity with some basic functional analytic objects and the motivation for studying them, such as the theory of normed linear spaces, or that every finite dimensional normed linear space has a unique normed linear topology, the construction of Fourier decompositions in Hilbert space, etc. A strong background in topology of metric spaces (say Rudin's Principles of Analysis) especially regarding completeness, is essential. But in theory someone who's never even heard of a "Banach space" before should be able to pick this book up and learn what's going on in a leisurely way while enjoying beautiful exposition and mathematical arguments and resulting theories. Also, Lax provides helpful bibliographical notes to the original literature at the end of each chapter.

Written by the former director of NYU's Courant Institute and a leading researcher in functional analysis, this monograph covers a broad range of topics. The comprehensiveness and depth of the work come at the cost of short proofs, sometimes more sketches of proofs. Being not so pleased about that at the beginning, I have really come to enjoy it: by concentrating on core ideas, one does not get distracted by technical details. Filling in the gaps has not been a problem so far, when I felt it was necessary. This makes the work both suitable for learning/teaching and as a reference.Understanding of the matter is greatly enhanced by many applications (which are still often in the area of pure mathematics): almost every theoretical chapter "XXX" is followed by a chapter "Applications of XXX". Due to the authors background, many applications concern partial differential equations.Finally, the book is beautifully written and a pleasure to read. I only regret that I didn't stumble upon it earlier.

This is a good book.

Graduate Course Functional Analysis TextbookI think it's good for every graduate student who wants to study functional analysis.It isn't biased toward specific topic. It covers general topics in functional analysis.Peter D. Lax is a genius! I am big fan of him:)

Great text. Maybe not for beginners. Assumes a decent analysis background.

This review is about the material quality of the printing in the copy I received. This is not about the content.I have access to a real copy of this edition in the local library. It is the usual high quality hardcover: it has a matte cover with texture, beautifully bound; the paper inside is high-quality, very soft and slightly off-white; and the printing of the text is very sharp. The version I received from Amazon was very different:- The hardcover was shiny, did not have texture, and had a natural tendency to bend strongly outwards, it even cannot stay opened if I leave it alone, it will close.- The paper inside is whiter, horribly white, like standard printing A4 paper;- The text printing looks like a cheap photocopy of the original. It don't even match a home laser printer. Some formulas are difficult to read. Moreover, some pages are not even centered.- Finally, the glue used is so cheap that it started to ungle!It looks and feels like a cheap knock-off photocopy done in a garage. When I pay a lot of money for a hardcover edition I want exactly what I have pay for, not a cheap knock-off. Authors should avoid their work being degraded with this cheap printing.

Compact book on functional analysis, but a lot more abstract than what I was expecting, so if you just want the introduction to the subject without much experience in advanced math, look elswhere! For example Introduction to functional analysis with applications by Kreyszig seems to be a Lot more relevant for physicists, with such a wide coverage of Hilbert and Banach spaces and with reminders about e.g. theorems in topology. This one does have Stone's theorem though.

Classic reference on functional analisys.