Elements of Hilbert Spaces and Operator Theory

Harkrishan Lal Vasudeva

ISBN 10: 9811097658 / ISBN 13: 9789811097652

Editore: Springer Nature Singapore, Springer Nature Singapore Jul 2018, 2018

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 536 pp. Englisch.

Codice articolo 9789811097652

Dati bibliografici

• Titolo: Elements of Hilbert Spaces and Operator Theory
• Editore: Springer Nature Singapore, Springer Nature Singapore Jul 2018
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 9811097658
• ISBN 13: 9789811097652
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 29 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 29 millimetri di profondità
• Peso: 803 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

HARKRISHAN LAL VASUDEVA had been a visiting professor of mathematics at Indian Institute of Science Education and Research, Mohali, India, between 2010 -2016. Earlier, he taught at Panjab University, Chandigarh, India, and held visiting positions in the University of Sheffield, the U.K., and the University of Graz, Austria, for research projects. He has numerous research articles to his credit in various international journals and has co-authored several books, two of which have been published by Springer.