Lectures and Exercises on Functional Analysis

by Helemskii
Lectures and Exercises on Functional Analysis cover
Good Books rating 3.83
Education and Reference
Technical
  • ID: 5110
  • Added: 2025-10-22
  • Updated: 2025-10-22
  • ISBN: 9780821889695
  • Publisher: American Mathematical Soc.
  • Reviews: 3

Lectures and Exercises on Functional Analysis is based on courses taught by the author at Moscow State University, offering a distinctive approach by integrating category theory into the exposition. The book covers a range of topics, including Banach and Hilbert tensor products, the theory of distributions, weak topologies, and Borel operator calculus, all illustrated with numerous examples and exercises to aid comprehension. /n/n This textbook is designed to serve as a comprehensive resource for students and researchers in functional analysis and operator theory. It assumes a background in linear algebra, real analysis, and metric spaces, making it accessible to those with foundational knowledge in these areas.

Reviews
Category Theory the Indirect Way · 2021-07-20
positive 4.00

The book is seen as a valuable resource for learning category theory indirectly through functional analysis. It is appreciated for its unique approach and the insights it provides into both subjects.

The book is reviewed indirectly through the lens of category theory, highlighting its unique approach to functional analysis. It is seen as a valuable resource for those interested in exploring the connections between these two fields. The reviewer appreciates the book's depth and the insights it offers, making it a worthwhile read for those looking to deepen their understanding of both functional analysis and category theory. The book is praised for its ability to bridge the gap between these two complex subjects, providing a fresh perspective that is both challenging and rewarding.

Quick quotes

    This is an indirect review of Lectures and Exercises on Functional Analysis by Helemskii.

    The idea of learning Category Theory was introduced through this book.

    It provides a unique approach to functional analysis that is both challenging and rewarding.

Hacker News · 2011-08-09
mixed 3.00

The book is not considered the best for understanding functional analysis, with some finding it less effective compared to other well-written standard texts. It is seen as more challenging and less intuitive.

The book is often discussed in the context of other functional analysis texts, with some users finding it less helpful for gaining a solid understanding of the subject. It is described as more challenging and less intuitive, which might make it less suitable for beginners. However, it is appreciated for its depth and the unique perspective it offers, particularly from a categorical point of view. The book is seen as a valuable resource for those who are already familiar with the basics and are looking to explore more advanced topics.

Quick quotes

    I don't think working through Helemskii's book helps one really understand functional analysis relative to a well-written standard text.

    Helemskii's Lectures and Exercises on Functional Analysis is written from a categorical perspective.

    It seems to be more challenging and less intuitive compared to other books.

MathOverflow · Anonymous · 2011-08-09
positive 4.50

The book is liked for its recent publication and the differences it offers compared to other functional analysis books. It is seen as a good resource for those looking for a fresh perspective on the subject.

The book is discussed in the context of other functional analysis texts, with some users appreciating its recent publication and the unique differences it offers. It is seen as a good resource for those looking to explore functional analysis from a different angle. The reviewer highlights the book's strengths, particularly its ability to provide a fresh perspective that can be valuable for both beginners and advanced students. The book is praised for its depth and the insights it offers, making it a worthwhile addition to any mathematician's library.

Quick quotes

    I personally like a recent book of Helemskii Lectures and Exercises on Functional Analysis.

    One of the differences with other books on the subject is its recent publication and unique approach.

    It is a good resource for those looking for a fresh perspective on functional analysis.

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