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A Course in Functional Analysis (Graduate Texts in Mathematics) [Englisch] [Taschenbuch]

John B. Conway

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Kurzbeschreibung

19. Februar 2010 1441930922 978-1441930927 Softcover reprint of hardcover 2nd ed. 1990

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general.

From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....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


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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

From the reviews of the second edition:

“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 … . This book is a comprehensive introduction to functional analysis. … I definitely recommend this book to anyone who really want/need to learn true functional analysis for graduate work.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013)


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Amazon.com: 3.7 von 5 Sternen  3 Rezensionen
5.0 von 5 Sternen Comprehensive and well-written 29. Mai 2013
Von Josue Rosario - Veröffentlicht auf Amazon.com
Format:Taschenbuch
This book is a comprehensive introduction to functional analysis. The style is very formal and rigorous (as it have to be) and you need to have a good background in measure theory and general topology (as it is mentioned in the introduction), chapters 1-4 & 6 of Folland's real analysis book would be more than enough. I think this background is necessary to fully appreciate this excellent book otherwise this book can be difficult and challenging. Do not forget that this book is designed to be used in grad courses. I definitely recommend this book to anyone who really want/need to learn true functional analysis for graduate work. Through its eleven chapters J. Conway masterfully wrote a beautiful exposition of this core subject.
Personally I have never been a follower of Rudin's books, I always have been able to find a substitute for every Rudin's book that match better my taste, and in this case Conway's functional analysis book is undoubtedly my choice. I consider that students interested in operator theory/algebras would appreciate this book even more, you can feel the operator taste throughout the book. Some negative remarks? well I think that the last chapter on Fredholm theory is a bit obscure, it can be largely improved, I would recommend chapter 1 of Gerald Murphy's book C*-algebras and operator theory for a cleaner and more meaningful exposition of Fredholm operators/index.
1 von 2 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen lovely 12. Januar 2011
Von the27th - Veröffentlicht auf Amazon.com
Format:Taschenbuch
I'm learning functional analysis from this book and it's absolutely wonderful. Clear, comprehensive, starts essentially from scratch (it assumes measure theory and linear algebra but nothing else) and deals in detail with what I think is a beautiful subject, the spectral theory of linear operators.
1 von 8 Kunden fanden die folgende Rezension hilfreich
1.0 von 5 Sternen Worst Book Ever! 17. August 2012
Von Tom Freeman - Veröffentlicht auf Amazon.com
Format:Taschenbuch
It was such shame to even have to have my eyes read the material in this book. Functional analysis is not hard. But, with Conway at the helm, this topic becomes so obfuscated. This text is written so poorly. The notation along is sub-standard, but moreover, there are no helpful examples that guide you to even minimal success in working out the exercises. Thank God for texts like Reed and Simon, Kreyzig, and Rudin. If it weren't for these texts, I would have never learned this subject---let alone, apply it in PDE. I am Complex Geometer. I need Geometric Analysis and PDE techniques, but I would never remotely recommend anyone in Math use this terrible book. It's truly disheartening that this book was picked by Springer. I guess, they've even lowered their standards for what constitutes a good publication. On that same note, I can only say completely negative things about Conway's Functions of One Complex Variable. Terrible as well. Such odd array of topics. That text does not allow for any transition to genus one curves: I mean, really, how can anyone reading that book intelligibly and without massive gaps make it in Several Complex Variables. I didn't care for the unnecessary discussions on approximation methods in complex analytic operator theory. Again, thank smart writers for books like Alhfors, and Rudin. At least, we know that true Complex Analysis subscribers use those books. I learned more Complex Analysis from Griffiths and Harris than that lackadaisical text of Conways'. Too bad. Largely, I can say with confidence that all of his books should not be read---no, no, must be avoided. Don't that charge appear on your account, but moreover, don't let his books ruin your shelves.
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