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Author : Nicolaas Pieter Dekker
Release : 1969
Genre : Linear operators
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Joint Numerical Range and Joint Spectrum of Hilbert Space Operators by : Nicolaas Pieter Dekker
Download or read book Joint Numerical Range and Joint Spectrum of Hilbert Space Operators written by Nicolaas Pieter Dekker. This book was released on 1969. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nicolaas Pieter Dekker
Release : 19??
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Joint numerical range and joint spectrum of hilbert space opera... by : Nicolaas Pieter Dekker
Download or read book Joint numerical range and joint spectrum of hilbert space opera... written by Nicolaas Pieter Dekker. This book was released on 19??. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hwa-Long Gau
Release : 2021-08-05
Genre : Mathematics
Kind : eBook
Book Rating : 606/5 ( reviews)
Book Synopsis Numerical Ranges of Hilbert Space Operators by : Hwa-Long Gau
Download or read book Numerical Ranges of Hilbert Space Operators written by Hwa-Long Gau. This book was released on 2021-08-05. Available in PDF, EPUB and Kindle. Book excerpt: Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.
Author : Kurt O. Friedrichs
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 964/5 ( reviews)
Book Synopsis Spectral Theory of Operators in Hilbert Space by : Kurt O. Friedrichs
Download or read book Spectral Theory of Operators in Hilbert Space written by Kurt O. Friedrichs. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.
Author : Samuel Kisengo
Release : 2011-10
Genre :
Kind : eBook
Book Rating : 522/5 ( reviews)
Book Synopsis Operator Theory by : Samuel Kisengo
Download or read book Operator Theory written by Samuel Kisengo. This book was released on 2011-10. Available in PDF, EPUB and Kindle. Book excerpt: This book is about numerical ranges and spectral properties of Hilbert space operators which have been of great interest to many mathematicians in the past decades. Nice properties with examples are explored. The properties of numerical range, for example, convexity and closedness are well known as proved in the classic Toeplitz - Hausdorff Theorem. In this book, we embark on the relationship between the spectrum and the numerical range of an operator, in particular, when the operator is normal. It is known that for a bounded linear operator on a Hilbert space, the spectrum is contained in the closure of its numerical range. For a normal operator, the numerical radius and the spectral radius coincides with the norm of the operator. These results are actually a contribution to the field of numerical ranges and spectra. For the reader to understand this book, it is paramount that a deep understanding of the theory of operators, especially on Hilbert spaces, General Topology, Functional Analysis and Abstract Algebra be put in place. This book is useful to both undergraduate students and postgraduate students.
