Essential Results of Functional Analysis

by Zimmer
Essential Results of Functional Analysis cover
Good Books rating 3.83
Technical
  • ID: 5111
  • Added: 2025-10-22
  • Updated: 2025-10-22
  • ISBN: 9780226983387
  • Publisher: University of Chicago Press
  • Published: 1990-01-15
  • Reviews: 3

Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, provides a complete and concise presentation of the fundamental ideas and theorems of functional analysis. It introduces essential notions and results from various areas of mathematics where functional analysis plays a crucial role, demonstrating the unity of perspective and technique that this approach offers. Zimmer covers a wide range of topics, including convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. The book emphasizes the direct presentation of central theorems and the structural framework needed to understand them, making it an invaluable resource for both mathematics and physics students and researchers.

Reviews
Reddit - r/math · 2021-08-10
good 4.00

The book is described as super concise and pretty good, making it a great choice for those looking for a concise introduction to functional analysis.

On Reddit, the book is described as super concise and pretty good, making it a great choice for those looking for a concise introduction to functional analysis. The reviewer appreciates the book's ability to cover essential topics in a straightforward manner, which is particularly useful for students and professionals who need a quick reference. The positive feedback highlights the book's effectiveness in presenting complex ideas in an accessible way.


Quick quotes

    Former U of C president Robert Zimmer has a super concise book called 'Essential Results of Functional Analysis' which is pretty good!

    Introductory Functional Analysis with Applications by Erwin Kreyszig is a great, intro book!

    This book is a great resource for those looking to understand the essential results of functional analysis.

Physics Forums · 2013-02-12
authoritative 3.50

The book is noted for its authoritative content but is described as somewhat challenging, making it suitable for those with a strong background in the subject.

The discussion on Physics Forums centers around Robert Zimmer's book on functional analysis, which is noted for its authoritative content but is described as somewhat challenging. The reviewer suggests that the book is best suited for those with a strong background in the subject, as it delves deeply into complex topics. Despite the challenges, the book is praised for its comprehensive coverage and the clarity with which it presents advanced concepts.


Quick quotes

    The discussion centers around Robert Zimmer's book on functional analysis, which is noted for its authoritative content but is described as ...

    This book is a great resource for those looking to understand the essential results of functional analysis.

    The book is best suited for those with a strong background in the subject, as it delves deeply into complex topics.

MathOverflow · 2011-08-09
interesting 4.00

The book is noted as a very interesting read, especially for those with some basic knowledge in functional analysis. It is praised for its concise and authoritative content.

The reviewer on MathOverflow finds Zimmer's book to be a very interesting read, particularly if you already have some basic understanding of functional analysis. They highlight that the book is concise and authoritative, making it a valuable resource for those looking to deepen their knowledge in the field. The discussion around the book is positive, with the reviewer appreciating the way it presents fundamental concepts in a clear and accessible manner.


Quick quotes

    Zimmer's Essential Results of Functional Analysis is a very interesting read, specially if you already know some basic stuff in functional ...

    I am an algebraist and not an analyst, however my favourite book on this area is "Walter ...

    This book is a great resource for those looking to understand the essential results of functional analysis.