Kindly note that we have put a lot of effort into researching the best books on Operator Theory 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 "Operator Theory" 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. “Introductory Functional Analysis with Applications” by E Kreysyig
“Introductory Functional Analysis with Applications” Book Review: This book is an introduction to functional analysis along with its applications. Main chapters included are metric space, normed spaces, banach spaces, Inner product spaces, Hilbert spaces. Other topics included are fundamental theorems for normed and banach spaces, Further applications on banach fixed point theorem, spectral theory of linear operators in normed spaces. All the equations and methods are discussed in a detailed manner. worked out examples on multiple topics are provided in this book. Students studying applied mathematics and graduate level engineering students can use this book.


2. “A Course in Operator Theory” by John B Coway
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“A Course in Operator Theory” Book Review: This book mentions the important topics of modern mathematics in operator theory. Main chapters included are introduction to C*algebra, Normal operators, compact operators, some nonnormal operators. Other topics mentioned are compact perturbations, Introduction to von Neumann algebra, reflexivity. Figures and examples are added to explain the topics. All the properties and theorems are discussed in detail. This book is useful for advanced mathematics and graduate level engineering students.


3. “Functional Analysis” by G Bachman and L Narici
“Functional Analysis” Book Review: This book mentions topics regarding functional analysis. Main chapters introduced are introduction to inner product spaces, orthogonal projections in the spectral theorem for normal transformations, normed spaces and metric spaces. Other topics mentioned are Isometrics and completion of a metric space, compactness in metric spaces, category and separable spaces. Detailed proofs of theorems and index of symbols are provided at the end of the book. This book is suitable for applied mathematics and graduate level engineering students.


4. “An Introduction to Topology and Modern Analysis” by G F Simmons  
5. “Problems in Operator Theory” by Y A Abramovich
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“Problems in Operator Theory” Book Review: This book discusses the main problems in operator theory. Chapters involved are odds and ends, basic operator theory, operators on AL and AM spaces, special classes of operators. Other topics included are integral operators, spectral properties, some special Spectra, positive matrices. all the theorems with proofs are provided in this book. exercises are also added for students to test their knowledge. This book is useful for research in physics, engineering, economics and finance.


6. “Recent Trends in Operator Theory and Partial Differential Equations” by Vladimir Maz’ya and David Natroshvili
“Recent Trends in Operator Theory and Partial Differential Equations” Book Review: This book discusses the recent trends in operator theory and partial differential equations. Chapters include various research papers published by renowned scientists. main chapters included are the dudu chava Roch formula, Convolution type operators, Higher frequency oscillators and many more. References are provided for further reading. This book is beneficial for applied mathematicians and researchers.


7. “Operator Theory: Part 4: A Comprehensive Course in Analysis” by Barry Simon
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“Operator Theory: Part 4: A Comprehensive Course in Analysis” Book Review: This book includes analysis on operator theory. Chapters discussed are the spectral theorem, the theorem of trace class and Fredholm Determinants, and the study of unbounded selfadjoint operators. Other topics included are introduction to the theory of orthogonal polynomials, banach algebras, compact abelian groups. All theorems and methods are supported by examples. This book is useful for advanced mathematics students.


8. “Topics in Operator Theory (Mathematical Surveys and Monographs)” by Carl M Pearcy
“Topics in Operator Theory (Mathematical Surveys and Monographs)” Book Review: This book discusses the Topics on operator theory. Chapters included are the theory of bounded linear operators, invariant subspace problem, infinite dimensional. Other topics mentioned are nontrivial invariant subspace, operator theory and classical analysis, weighted shift operators and analytical function theory. Plenty of theorems and new concepts are covered in this book. This book is useful for advanced mathematics students.


9. “Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics)” by Ronald G Douglas
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“Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics)” Book Review: This book mentions the advanced topics in operator theory. Chapters discussed are general topology, measure theory, algebra, analytical function theory. Every chapter concludes with source notes and additional reading comments. A large number of problems are discussed to test the knowledge of students. This book is useful for graduate level students.


10. “Operator Theory: Nonclassical Problems” by S G Pyatkov
“Operator Theory: Nonclassical Problems” Book Review: This book discusses the mathematical method applicable on nonclassical problems of mathematical physics. Major chapters included are indefinite inner product spaces, Spectral theory for linear selfadjoint pencils, Elliptic eigenvalue problems with an indefinite weight function. Other topics included are operator differential equations, the fourier method, some applications to partial differential equations. A huge number of problems are solved to explain the topics easily. Plenty of exercises are provided for students to practice. This book is suitable for advanced mathematics students.


11. “Recent Advances in Matrix and Operator Theory (Operator Theory: Advances and Applications)” by Joseph A Ball and Yuli Eidelman
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“Recent Advances in Matrix and Operator Theory (Operator Theory: Advances and Applications)” Book Review: This book provides the recent developments in the field of matrix and operator theory. main topics included are inverse problems for first order discrete systems, stability of dynamic systems via semidefinite programming, image of a Jacobi field. Other topics mentioned are generalization to ordered groups of a krein theorem, the numerical range of a class of selfadjoint operator functions, the Eigen structure of complex symmetric operators. All the papers mentioned at the international workshop on operator theory and its applications held in Connecticut in July 2005 are mentioned in this book. This book is beneficial for advanced mathematics students and researchers.


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