Best Reference Books – Functional Analysis

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We have compiled the list of Top 10 Best Reference Books on Functional Analysis subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Functional Analysis along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Functional Analysis subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Functional Analysis" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Introduction to Topology and Modern Analysis” by G F Simmons

“Introduction to Topology and Modern Analysis” Book Review: This book extensively covers the mathematical aspects of continuity and linearity. After explaining their basic definition, the book explores their relationship to each other in terms of topology and modern analysis. Students, researchers, and professionals can refer to this book.

2. “Functional Analysis” by G Bachman and L Narici

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“Functional Analysis” Book Review: This book introduces the inner-product spaces, normed and metric spaces, and topological spaces in great detail. Complete orthonormal sets, the Hahn-Banach theorem and its consequences are also covered. Subsequent chapters deal with spectral notions, square roots, a spectral decomposition theorem, etc. Detailed proofs of theorems, definitions, index of symbols, and end-of-chapter exercises are also included. Students with background in linear algebra, advanced calculus, physics and engineering can refer to this book.

3. “Introduction to Functional Analysis” by A E Taylor

“Introduction to Functional Analysis” Book Review: This book systematically analyzes the theory of normed linear spaces and linear mappings between such spaces. Separate chapters on Banach algebras, the Krein-Milman theorem, weak topologies and duality, equicontinuity, and the theory of Fredholm operators provided. Recent advances in functional analysis are also included with special focus on closed unbounded linear operators. The unifying power of the abstract linear-space is studied using problems of linear algebra, classical analysis, and differential and integral equations. Illustrations are drawn from ordinary differential equations.

4. “Functional Analysis” by B V Limaye

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“Functional Analysis” Book Review: This book is divided into two sections and introduces a distance structure on a linear space with additional features. The first section covers normed spaces, their completeness and continuous linear maps on them including the theory of compact operators. Meanwhile, the second section deals with Hilbert spaces and spectral theorems for compact self-adjoint operators. Numerous examples and problems of varying levels of difficulty are provided to illustrate abstract concepts and applications of results. The approximate construction of a solution is also indicated along with its existence and uniqueness.

5. “Introductory Functional Analysis with Applications” by Erwin Kreyszig

“Introductory Functional Analysis with Applications” Book Review: This book explores the application of functional analysis to the practical study of natural sciences and mathematics. The book concentrates on the fundamental concepts, principles, methods, and major applications of functional analysis. Numerous problems on Hilbert space theory and Banach spaces are also solved in this text to provide a better understanding of the subject.

6. “Functional Analysis” by P K Jain

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“Functional Analysis” Book Review: This book introduces the fundamentals of real analysis, linear algebra, and metric spaces along with the uniform notations in the initial chapters. This is followed by discussions on normed and Banach spaces, bounded linear operators and bounded linear functionals. Subsequent chapters deal with the theory and specific geometry of Hilbert spaces, functionals and operators on Hilbert spaces. Separate chapters on spectral theory and Schauder bases are also included. This book is designed for senior undergraduate- and graduate-level students.

7. “Functional Analysis: A First Course” by Nair

“Functional Analysis” Book Review: The book presents a concise treatment of functional analysis using various figures and examples. After discussing linear algebra and linear space, the book introduces operators and some basic theorems of functional analysis. Advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators are also addressed. The theorems are then applied and related to problems which arise while solving operator equations. This book is ideal for the postgraduate students in Mathematics.

8. “Functional Analysis” by B V Limaye

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“Functional Analysis” Book Review: This book is divided into two sections and introduces a distance structure on a linear space with additional features. The first section covers normed spaces, their completeness and continuous linear maps on them including the theory of compact operators. Meanwhile, the second section deals with Hilbert spaces and spectral theorems for compact self-adjoint operators. Numerous examples and problems of varying levels of difficulty are provided to illustrate abstract concepts and applications of results. The approximate construction of a solution is also indicated along with its existence and uniqueness.

9. “Functional Analysis” by Walter Rudin

“Functional Analysis” Book Review: This book presents a modern take of functional analysis from the analysis and applied mathematics perspective. Advanced topics like Lamonosov’s invariant subspace theorem, Kakutani’s fixed point theorem, and an ergodic theorem are also explained in detail. Replete with examples and exercises, this text is suitable for graduate courses in functional analysis.

10. “Textbook of Functional Analysis: A Problem-Oriented Approach” by Krishnan V K

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“Textbook of Functional Analysis” Book Review: This book explains and demonstrates the use of the fundamental theorems in functional analysis through solved numerical problems in a comprehensive manner. Solved numerical problems related to the spectral properties of compact operators on Banach spaces and Hilbert spaces are also included for thorough practice. Problems based on the square root of a positive operator are also provided along with exercise sets for the readers to solve. This is a suitable book for students pursuing postgraduate courses in mathematics.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Functional Analysis – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on "Functional Analysis" so that one can readily see the list of top books on "Functional Analysis" and buy the books either online or offline.

If any more book needs to be added to the list of best books on Functional Analysis subject, please let us know.

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