**Best Reference Books on Operator Theory**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Operator Theory Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Operator Theory below.

1."A Course in Operator Theory" by John B Coway
“A Course in Operator Theory” Book Review: This book covers important topics in operator theory within modern mathematics. The main chapters consist of an introduction to C*-algebra, normal operators, compact operators, and some non-normal operators. Additionally, compact perturbations, an introduction to von Neumann algebra, and reflexivity are also addressed. The book contains figures and examples to aid in explaining the concepts, and all properties and theorems are discussed in detail. It is an ideal resource for advanced mathematics and graduate level engineering students.
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2."Problems in Operator Theory" by Y A Abramovich
“Problems in Operator Theory” Book Review: This book delves into the primary problems found in operator theory. The chapters include “odds and ends,” basic operator theory, operators on AL and AM spaces, and special classes of operators. Furthermore, integral operators, spectral properties, some special spectra, and positive matrices are also discussed. The book provides all theorems with proofs, along with exercises to allow students to test their knowledge. It is a valuable resource for research in physics, engineering, economics, and finance.
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3."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 explores recent trends in operator theory and partial differential equations through various research papers published by renowned scientists. The main chapters cover the dudu chava Roch formula, convolution type operators, higher frequency oscillators, and more. References are provided for further reading, and the book is beneficial for applied mathematicians and researchers.
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4."Operator Theory: Part 4: A Comprehensive Course in Analysis" by Barry Simon
“Operator Theory: Part 4: A Comprehensive Course in Analysis” Book Review: This book analyzes operator theory through the study of the spectral theorem, the theorem of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. Additionally, it covers an introduction to the theory of orthogonal polynomials, Banach algebras, compact abelian groups, and supports all theorems and methods with examples. This book is useful for advanced mathematics students.
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5."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 topics in operator theory, including the theory of bounded linear operators, the invariant subspace problem, and infinite dimensional spaces. Additionally, non-trivial invariant subspaces, operator theory and classical analysis, weighted shift operators, and analytical function theory are also mentioned. A plethora of theorems and new concepts are covered in the book, making it valuable for advanced mathematics students.
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6."Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics)" by Ronald G Douglas
“Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics)” Book Review: This book covers advanced topics in operator theory, including general topology, measure theory, algebra, and analytical function theory. Every chapter concludes with source notes and additional reading comments, and a large number of problems are discussed to test the knowledge of students. This book is useful for graduate level students.
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7."Operator Theory: Nonclassical Problems" by S G Pyatkov
“Operator Theory: Nonclassical Problems” Book Review: This book examines mathematical methods applicable to non-classical problems in mathematical physics. Major chapters include indefinite inner product spaces, spectral theory for linear self-adjoint pencils, and elliptic eigenvalue problems with an indefinite weight function. Additionally, operator differential equations, the Fourier method, and some applications to partial differential equations are also discussed. A significant number of problems are solved to aid in comprehension, and numerous exercises are provided for students to practice. This book is suitable for advanced mathematics students.
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8."Recent Advances in Matrix and Operator Theory (Operator Theory: Advances and Applications)" by Joseph A Ball and Yuli Eidelman
“Recent Advances in Matrix and Operator Theory (Operator Theory: Advances and Applications)” Book Review: This book provides recent developments in the field of matrix and operator theory. Main topics include inverse problems for first order discrete systems, stability of dynamic systems via semidefinite programming, and the image of a Jacobi field. Additionally, it mentions the generalization to ordered groups of a Krein theorem, the numerical range of a class of self-adjoint operator functions, and the eigenstructure of complex symmetric operators. All papers presented at the international workshop on operator theory and its applications held in Connecticut in July 2005 are included in this book, making it beneficial for advanced mathematics students and researchers.
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