Linear Functional Analysis (Springer Undergraduate Mathematics Series) 2nd Edition by Bryan Rynne (PDF)

Description

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Lots of examples, very helpful exercises (not too many). Can be used as self-study, supplement or prerequisite for more general and advanced functional analysis

⭐Clear exposition, loads of examples and a surprising number of topics. This book served as an excellent supplement to Rudin and would probably serve the self-study student quite well as a place to learn of the beautiful theory.

⭐I highly recommend this book for independent study or as a supplement to a text. You can see if you’re on the right track with exercises because the text has solutions and hints in the back. People must keep in mind that this book focuses on linear functional analysis and not functional analysis in general.

⭐Muy buen servicio quedé completamente satisfecho, por eso me guata comprar en Amazon.com siempre que he comprado me ha gustado el servicio.

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⭐This undergrad text is extremely clear, with lots of examples and exercises. I thought the coverage was a bit limited, even for an undergrad text and the writing style is kind of dry. Still, it’s perhaps even easier than Kreyszig.

⭐Out of the several books on Functional Analysis available, this is the easiest and most accessible, and is suitable for undergraduates. But, you still need to know some prerequisite material, including linear algebra, analysis, measure theory and Lebesgue integration. In case you have forgotten, this is helpfully summarised in chapter 1. I had not studied measure theory before, but this book makes it sound so beautiful and fascinating, that I hope to investigate further. The next part of the book deals with Banach and Hilbert spaces, the fundamental ideas of Functional Analysis. Then it tells you about operators, which is where matters get interesting! An operator is basically a function from one space to another, but in some situations, the set of operators form their own space! Chapter 5 deals with linear operators on Hilbert spaces, and here things just get beautiful! It defines the spectrum of an operator, which is a subset of the complex numbers, simliar to the set of eigenvalues in linear algebra. So many wonderful things follow on so easily. The book goes on to deal with compact operators, a special type of operator. Finally, it explains how Functional Analysis can help you solve differential and/or integral equations, but the study of the subject is worthwhile in its own right. The exercises in this book are very challenging, which is good because it makes you really think about the material, and the authors have helpfully provided model answers. Having finished this book, the reader could then go onto a more advanced book on the topic, and a list of suggested reading is provided at the end. Ultimately, this is a very good book on Functional Analysis, full of useful information for the mathematician, and it shows you how far Analysis, as a subject, extends beyond the basic idea of “a more rigorous version of single-variable calculus”. Heartily recommended!

⭐A useful book to help with learning Topology and continues to Functional Analysis which is useful for a mathematics student! Have used this book quite often since buying it as it is easy to follow and understand. Haven’t found a Springer Undergraduate book that hasn’t been useful as of yet!

⭐This book is very interesting, it is written is very clever way, with many examples, it is well organized and useful.

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