Abstract
The recent interest in ε-pseudospectra of operators results from their (in comparison with usual spectra) excellent continuity properties. The goal of the present paper is to introduce and to examine ε-pseudospectra of operator polynomials with main emphasis on the continuity aspect.
Dedicated to Professor Israel C. Gohberg on the occasion of his 70th birthday
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Böttcher, Pseudospectra and singular values of large convolution operators, J. Integral Equations and Appl. 6 (1994), 267–301.
A. Böttcher and B. Silbermann, The finite section method for Toeplitz operators on the quarter-plane with piecewise continuous symbols, Math. Nachr 110 (1983), 279–291.
A. Böttcher and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices, Springer-Verlag, New York, Berlin, Heidelberg 1999.
R. Hagen, S. Roch and B. Silbermann, Spectral Theory of Approximation Methods for Convolution Equations, Birkhäuser Verlag, Basel, Boston, Berlin 1995.
R. Hagen, S. Roch and B. Silbermann, C* -algebras and Numerical Analysis, Textbook in preparation.
H. Landau, On Szegö’s eigenvalue distribution theorem and non-Hermitian kernels, J. Anal. Math. 28 (1975), 335–357.
H. Landau, The notion of approximate eigenvalues applied to an integral equation of laser theory, Q. Appl. Math., 1977, 165–171.
L. Reichel and L.N. Trefethen, Eigenvalues and pseudo-eigenvalues of Toeplitz matrices, Linear Algebra Appl. 162 (1992), 153–185.
S. Roch and B. Silbermann, C*-algebra techniques in numerical analysis, J. Oper. Theory 35 (1996), 241–280.
L. Rodman, An Introduction to Operator Polynomials, Birkhäuser Verlag, Basel, Boston, Berlin 1989.
B. Silbermann, Symbol constructions in numerical analysis, In: Petkov, V, Lazarov, R. (Eds.): Integral equations and inverse problems, Pitman Research Notes in Mathematics Series 235 (1991), 241–252.
L.N. Trefethen, Pseudospectra of matrices, In: D.E Griffiths, G.A. Watson (Eds.), Numerical Analysis 1991, Longman, 1992, 234–266.
L.N. Trefethen, Non-normal matrices and pseudospectra, Monograph in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Roch, S. (2001). Pseudospectra of Operator Polynomials. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8323-8_25
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9516-3
Online ISBN: 978-3-0348-8323-8
eBook Packages: Springer Book Archive