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The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators.
The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
List of contents
Spectrum of an operator.- Continuous functional calculus.- Positive operators.- Spectral theorems and functional calculus.- Compact operators.- The trace.- Functional calculus for families of operators.- Operators and their graphs.- z-transform.- Spectral theorems.- Self-adjoint extensions of symmetric operators.- One-parameter groups of unitary operators.- Appendices.- Index of notation.- References - Index.
Summary
The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators.
The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
Additional text
“We warmly recommend the book to students interested in operator theory and many of its significant applications.” (Valentin Keyantuo, Mathematical Reviews, November, 2019)
“The book under review is a solid and concise textbook for advanced undergraduate and masters students. ... It is all in all an excellent book and the reviewer would definitely recommend it to anybody who wants to learn the theory of (bounded as well as unbounded) linear operators on Hilbert spaces.” (Jaydeb Sarkar, zbMath 1417.47001, 2019)
Report
"We warmly recommend the book to students interested in operator theory and many of its significant applications." (Valentin Keyantuo, Mathematical Reviews, November, 2019)
"The book under review is a solid and concise textbook for advanced undergraduate and masters students. ... It is all in all an excellent book and the reviewer would definitely recommend it to anybody who wants to learn the theory of (bounded as well as unbounded) linear operators on Hilbert spaces." (Jaydeb Sarkar, zbMath 1417.47001, 2019)
