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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

Small Rank Perturbations of H-Expansive Matrices

Authors : G. J. Groenewald, D. B. Janse van Rensburg, A. C. M. Ran

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

Publisher: Springer Nature Switzerland

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Abstract

In this paper small rank perturbations of H-expansive and H-unitary matrices are explored. Particular attention is given to the location of eigenvalues with respect to the unit circle for these classes of matrices. The canonical form (in the H-unitary case) and the simple form (in the H-expansive case) for the pair \((A,H)\) will be the starting point.

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previous chapter On Non-commutative Spreadability
next chapter On the Berger-Coburn Phenomenon
Literature
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H. Bart, I. Gohberg, M.A. Kaashoek, A.C.M. Ran, Factorization of Matrix and Operator Functions: The State Space Method. Operator Theory: Advances and Applications, vol. 178 (Birkhäuser Verlag, Basel, 2008)
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H. Bart, I. Gohberg, M.A. Kaashoek, A.C.M. Ran, A State Space Approach to Canonical Factorization with Applications. Operator Theory: Advances and Applications, vol. 200 (Springer Science & Business Media, Berlin, 2010)
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C. Mehl, V. Mehrmann, A.C.M. Ran, L. Rodman, Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations. BIT. Numer. Math. 54, 219–255 (2014)MathSciNetCrossRef
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A.C.M. Ran, A note on the structure of expansive matrices in indefinite inner product spaces. Linear Algebra Appl. 655, 291–301 (2022)MathSciNetCrossRef
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A.C.M. Ran, M. Wojtylak, Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices. Complex Anal. Oper. Theory 15, 44 (2021)MathSciNetCrossRef
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Metadata
Title
Small Rank Perturbations of H-Expansive Matrices
Authors
G. J. Groenewald
D. B. Janse van Rensburg
A. C. M. Ran
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_8

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