Numerical Ranges of Hilbert Space Operators

This book develops the 100-year-old numerical range theory starting with the basics of operator theory and matrix analysis.

Hwa-Long Gau (Author), Pei Yuan Wu (Author)

9781108479066, Cambridge University Press

Hardback, published 5 August 2021

502 pages
24 x 15.9 x 2.6 cm, 0.94 kg

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK], Algebra [PBF]