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# đź“™ Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva â€” free epub

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The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators.

In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

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In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

- Author:
**Harkrishan Lal Vasudeva** - Year:
**2017** - Publisher:
**Springer** - Language:
**English** - ISBN:

- File size:
**4 067 835** - Format:
**pdf**

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This course-tested book explains in detail the theory of linear Hilbert-space operators and their use in quantum physics. The central mathematical tool of the book is the spectral theory of self-adjoint operators; in order to make the exposition self-cont...

This course-tested book explains in detail the theory of linear Hilbert-space operators and their use in quantum physics. The central mathematical tool of the book is the spectral theory of self-adjoint operators; in order to make the exposition self-cont...

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such...

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such...

This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results withÂ aÂ wide variety ofÂ exercises that range from theÂ straightforward to the state-of-the-art.Â Complete solutions to allÂ pro...

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that ...

Physics has long been regarded as a wellspring of mathematical problems. "Mathematical Methods in Physics" is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics tha...

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that ...

This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is...

This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowenâ€“Douglas operators is...