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Weighted Hardy Spaces Over the Unit Ball: The Freely Noncommutative and Commutative Settings Read chapter Read first chapter

2024 | OriginalPaper | Chapter

Kippenhahn’s Construction Revisited

Author : Stephan Weis

Published in: Operator and Matrix Theory, Function Spaces, and Applications

Publisher: Springer Nature Switzerland

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Abstract

Kippenhahn discovered that the numerical range of a complex square matrix is the convex hull of a plane real algebraic curve. Here, we present an example of a convex set, which has a similar algebraic description as the numerical range, whereas the analogue of Kippenhahn’s construction fails regarding isolated, singular points of the curve. This example prompted us to carefully review Kippenhahn’s assertion and to highlight aspects of a complete proof that was achieved with methods of convex geometry and real algebraic geometry.

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previous chapter Composition in Reproducing Kernel Hilbert Spaces à Rebours
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Appendix
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Metadata
Title
Kippenhahn’s Construction Revisited
Author
Stephan Weis
Copyright Year
2024
Book
Operator and Matrix Theory, Function Spaces, and Applications

Print ISBN: 978-3-031-50612-3

Electronic ISBN: 978-3-031-50613-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-50613-0_18

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