Numerical Ranges of Hilbert Space Operators

Hwa-Long Gau · Pei Yuan Wu

Aug. 2021 · Encyclopedia of Mathematics and its Applications Boek 179 · Cambridge University Press

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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.

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Hwa-Long Gau is Professor in the Department of Mathematics at National Central University, Taiwan. Together with Pei Yuan Wu, he has co-authored over 40 publications on numerical range problems. One of them, Zero-dilation index of a finite matrix (2014), is currently the most-downloaded article in 'Linear Algebra and its Applications'.

Pei Yuan Wu is Professor Emeritus in the Department of Applied Mathematics of National Chiao Tung University. He has been working in operator theory and matrix analysis for 45 years, recently focusing on the numerical ranges of operators and matrices. He was awarded the 16th Béla Szőkefalvi-Nagy Medal by the Bolyai Institute of University of Szeged in 2015.