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Functional Analysis
Funktionalanalysis f�r Fortgeschrittene: Hier erfahren Sie alles �ber Topologie, lineare Operatoren, die Gelfandsche Theorie kommutativer Banach-Algebren und vieles andere. Mit durchgerechneten Beispielen und �bungsaufgaben!
608 pages, Hardcover
First published April 4, 2002
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About the author
Peter D. Lax
47 books7 followersPeter David Lax was a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.
Lax has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields.
In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.
Lax has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields.
In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.
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Displaying 1 - 4 of 4 reviews
December 8, 2021
(~3.5 stars, rounded down)
I didn't like this book at all (though I did still enjoy reading it somewhat, because of the good company), as a book to learn functional analysis from. It has much to recommend it as a reference volume, though, and as a tool for review of this material, for someone who has already mastered it.
The book is less pedagogical than it could (should?) be, and that's putting it mildly. I cannot stress enough that THIS BOOK HAS NO PICTURES IN IT (which I don't know how to forgive). What it _does_ have is an impressively large and diverse array of theorems and examples. It also has plenty of exercises, but these come with little to no guidance, and no indication of their difficulty levels (which seem to vary unpredictably; I found most very challenging, though).
I frequently found my eyes glazing over, and a big part of that is probably because I was slightly under-prepared (analysis-wise) to read this book. I will probably find this book much more useful after I learn more functional analysis from more pedagogical sources, at which point a less negligible fraction of the huge collection of examples might become interesting and relevant to me.
I didn't like this book at all (though I did still enjoy reading it somewhat, because of the good company), as a book to learn functional analysis from. It has much to recommend it as a reference volume, though, and as a tool for review of this material, for someone who has already mastered it.
The book is less pedagogical than it could (should?) be, and that's putting it mildly. I cannot stress enough that THIS BOOK HAS NO PICTURES IN IT (which I don't know how to forgive). What it _does_ have is an impressively large and diverse array of theorems and examples. It also has plenty of exercises, but these come with little to no guidance, and no indication of their difficulty levels (which seem to vary unpredictably; I found most very challenging, though).
I frequently found my eyes glazing over, and a big part of that is probably because I was slightly under-prepared (analysis-wise) to read this book. I will probably find this book much more useful after I learn more functional analysis from more pedagogical sources, at which point a less negligible fraction of the huge collection of examples might become interesting and relevant to me.
November 29, 2021
Not perfect, and I didn't read every page, but it is better than the other sources I've found on functional analysis. The book up to and including the Krein-Milman Theorem part were very good (and some parts after that did shine still). Later it had worse typo-checking. Recommend it, even if partially by a process of elimination. Many of the examples were very useful to me.
June 20, 2022
I haven't read all of it, but I've read a big part of it, including pretty much everything that deals with unbounded operators.
It's by far the worse functional analysis book I've ever read.
Many of the proofs are unnecessarily complicated, and some of his statements are non-sensical, e.g. "open compact manifold" when he talks about the Koopman group.
As part of the definition of "open manifold" is "non-compact"...
And there's more like this.
The author also sometimes uses notation and terminology that are different that what is usually met in the literature, which can make things very confusing.
His section on the unbounded functional calculus is the worse and most inadequate treatment of the subject I have ever encountered.
The only thing that has stood out in this book is that every theorem that is named something-Lax-something, seems to have been included.
Overall, probably okay as a reference - provided the reader is willing to double check for errors - , but not much else.
It's by far the worse functional analysis book I've ever read.
Many of the proofs are unnecessarily complicated, and some of his statements are non-sensical, e.g. "open compact manifold" when he talks about the Koopman group.
As part of the definition of "open manifold" is "non-compact"...
And there's more like this.
The author also sometimes uses notation and terminology that are different that what is usually met in the literature, which can make things very confusing.
His section on the unbounded functional calculus is the worse and most inadequate treatment of the subject I have ever encountered.
The only thing that has stood out in this book is that every theorem that is named something-Lax-something, seems to have been included.
Overall, probably okay as a reference - provided the reader is willing to double check for errors - , but not much else.
October 28, 2008
interesting historical notes
Displaying 1 - 4 of 4 reviews