Numerical Ranges of Hilbert Space Operators

ISBN-13: 9781108479066 / Angielski / Twarda / 2021 / 502 str.

Taiwan) Hwa-Long Gau (National Central University; Taiwan) Pei Yuan Wu (National Chiao Tung University

Opis

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.

Recenzje

All in all, this is a well-written and useful book dedicated to a special subject in the realm of single operator theory, which will be helpful to every working mathematician somehow involved with numerical range, as well as to graduate students going into this research field. I have kept my copy on that special bookshelf near my desk within hands' reach.' Carlos S. Kubrusly, zbMATH Open

Spis treści

Preface; 0. Preliminaries in Operator Theory; 1. Numerical Range; 2. Numerical Ranges of Special Operators; 3. Numerical Contraction; 4. Algebraic and Essential Numerical Ranges 5. Numerical Range and Dilation; 6. Numerical Range of Finite Matrix; 7. Numerical Range of Sn-Matrix; 8. Generalized Numerical Ranges; Appendix: Convex Set.