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Numerical Ranges of Hilbert Space Operators

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Numerical Ranges of Hilbert Space Operators

Numerical Ranges of Hilbert Space Operators

Hwa-Long Gau, National Central University, Taiwan
Pei Yuan Wu, National Chiao Tung University, Taiwan
October 2021
Hardback
9781108479066
$158.00
USD
Hardback
    Description

    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.

    • Starts from scratch with an introduction to operator theory and matrix analysis then gradually builds up the whole numerical range theory
    • Detailed bibliography encourages the reader to explore the wider literature
    • Contains over 400 problems ranging from routine exercises to research results in the published papers

    Reviews & endorsements

    '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

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    Contents

    Table of Contents

    • 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.
      • Show more
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    About the authors
      Authors
    • Hwa-Long Gau , National Central University, Taiwan

      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 , National Chiao Tung University, Taiwan

      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.

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