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Stability of sums of operators

Stability of sums of operators A linear operator is said to be stable (Hurwitzian) if its spectrum is located in the open left half-plane. We consider the following problem: let A and B be bounded linear operators in a Hilbert space, and A be stable. What are the conditions that provide the stability of $$A+B$$ A + B ? http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

Stability of sums of operators

Gil’, Michael
ANNALI DELL'UNIVERSITA' DI FERRARA , Volume 62 (1) – Apr 21, 2016
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Publisher
Springer Journals
Copyright
Copyright © 2016 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-016-0243-1
Publisher site
See Article on Publisher Site

Abstract

A linear operator is said to be stable (Hurwitzian) if its spectrum is located in the open left half-plane. We consider the following problem: let A and B be bounded linear operators in a Hilbert space, and A be stable. What are the conditions that provide the stability of $$A+B$$ A + B ?

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Apr 21, 2016

References

  • Stability of Solutions of Differential Equations in Banach Space
    Daleckii, YL; Krein, MG
  • Eigenvalues of sums of pseudo-hermitian matrices
    Foth, P
  • Operator Functions and Localization of Spectra, Lecture Notes in Mathematics
    Gil’, MI
  • A bound for condition numbers of matrices
    Gil’, MI
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    Helmke, U; Rosenthal, J
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    Horn, A
  • Spectral polyhedron of the sum of two Hermitian matrices
    Lidskii, BV
  • Diagonals and eigenvalues of sums of Hermitian matrices. Extreme cases
    Miranda, H
  • Eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions
    Peacock, MJM; Collings, IB; Honig, ML
  • On the eigenvalues of a sum of Hermitian matrices
    Thompson, RC; Freede, L