Kindly note that we have put a lot of effort into researching the best books on Operators On Hilbert Spaces 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 "Operators On Hilbert Spaces" 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. “Functional Analysis” by B V Limaye
“Functional Analysis” Book Review: The book presents basic concepts and major aspects of functional analysis. The initial section of the book features normed spaces and their completeness, continuous linear maps, and theory of compact operators. Moving on, the chapters based on inner product spaces and spectral theorem are included. The topics like fixed points, extreme points, SturmLiouville problems, and unbounded operators are thoroughly explained. The content of this book is supported by several examples and problems. The further scope of development in the areas related to functional analysis is highlighted in this book.


2. “Functional Analysis” by K Yoshida
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“Functional Analysis” Book Review: The book begins with a presentation on set theory, topological spaces, measure spaces, and linear spaces. Moving on to Seminorms, a general theory of Banach and Hilbert spaces and the theory of generalized functions is clearly presented. The chapters feature analytical theory of semigroups, ergodic theory and diffusion theory, integration of the equation of evolution, weak topologies, and duality in locally convex spaces and nuclear spaces. The applications of functional analysis in various fields of modern and classical analysis are highlighted in this book. The book is basically for the graduating students of mathematics but will be equally important for the researchers related to pure and applied mathematics.


3. “First Course in Functional Analysis” by G Goffman and G Pedrick  
4. “Introduction to Functional Analysis” by A Taylor and D Lay
“Introduction to Functional Analysis” Book Review: The book is a great source of information of functional analysis and provides an essential foundation for further study in distinct areas of analysis. A basic theory on normed linear spaces and linear mappings is presented in this text. The topics like Banach algebras, weak topologies and duality, equicontinuity, KreinMilman theorem, Fredholm operators, and closed unbounded linear operators are thoroughly explained. The book introduces many techniques and methodologies for dealing with the problems of linear algebra, classical analysis, and differential and integral equations. The recent developments in the field of functional analysis are addressed in this book.
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5. “Theory of Linear Operators in Hilbert Space” by N I Akhiezer and I M Glazman
“Theory of Linear Operators in Hilbert Space” Book Review: The book aims at introducing linear operators in Hilbert space. The geometry of Hilbert space and the spectral theory of unitary and selfadjoint operators are discussed in detail. The chapters of this book cover all the major topics related to Hilbert space, linear functional, bounded linear operators, projection operators, unitary operators, theory of linear operators, and spectral analysis. The book will be an asset for the graduate and advanced undergraduate students of mathematics. The mathematicians and physicists will also find this book useful.


6. “Operators on Hilbert Space” by V S Sunder
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“Operators on Hilbert Space” Book Review: The book features a clear presentation on the theory of bounded linear operators on separable Hilbert space. It reflects the spectral theorem with respect to unique, continuous, and measurable functional calculus.The chapters of this book are selfcontained, and explain topics like Gelfand theory of commutative Banach algebras, von NeumannSchatten ideals, compact operators, traceclass operators, and all bounded operators, quite efficiently. The book will be beneficial for the students and professionals of mathematics and physics.


7. “Harmonic Analysis of Operators on Hilbert Space” by Béla Sz Nagy and Ciprian Foias
“Harmonic Analysis of Operators on Hilbert Space” Book Review: The book is an updated and revised piece of work featuring latest topics and recent developments in the field of harmonic analysis and Hilbert space. The chapters feature study of two operator classes, operators with noninjective functional calculus, structure, classification, and invariant subspaces. The final section of the book is devoted to the latest and ongoing developments in the field of harmonic analysis. The book will be a great reference for the students and professionals related to mathematics, interpolation theory, and control theory. It will be a good source of information for contraction operators.


8. “Spectral Theory of Operators on Hilbert Spaces” by Carlos S Kubrusly
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“Spectral Theory of Operators on Hilbert Spaces” Book Review: The book covers all the major aspects and latest topics of spectral theory of Hilbert space operators. The chapters of this book efficiently explain all the essential topics related to preliminaries, spectrum, spectral theorem, functional calculus, and Fredholm theory. To give better practical knowledge and relatable content to the readers, the applications of Hilbert space operators and spectral theory in various fields are highlighted. The book will be a valuable resource for students graduating in mathematics, statistics, economics, engineering, and physics.


9. “Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space” by Takayuki Furuta
“Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space” Book Review:The book focuses on the recent research and results on linear operators on a Hilbert space. The basic properties and fundamental principles of Hilbert space are clearly mentioned. The chapters of this book are wellstructured, precise, and describe the properties of bounded linear operators before addressing the developments and scope of research in bounded linear operators. The book uses matrix theory as a tool for clear explanation with many featured methods and theorems. The book will be useful for the students and researchers of mathematics.


10. “Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrödinger Equations” by Samuel S Holland Jr
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“Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrödinger Equation” Book Review: The book aims at introducing the very basics of Hilbert space theory and Hermitian differential operators. The chapters of this book revolve around first and second order linear differential equations, eigenvalues and eigenfunctions of classical Hermitian differential operators, general theory of orthogonal bases in Hilbert space, and Schrödinger’s equations. The book highlights Fourier transform as a unitary operator and illustrates the applications of various differentiation and integration techniques. Many worked examples and exercises are included in this text for selfstudy and selfassessment of the readers. The book will be suitable for the students of applied mathematics, physics, and engineering. It will be equally important for the applied mathematicians, physicists, and theoretical engineers.


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