Inner bounds for the spectrum of quasinormal operators
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Abstract:
A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.References
- M. S. Brodskiĭ, Triangular and Jordan representations of linear operators, Translations of Mathematical Monographs, Vol. 32, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin. MR 0322542
- Michael I. Gil′, Norm estimations for operator-valued functions and applications, Monographs and Textbooks in Pure and Applied Mathematics, vol. 192, Marcel Dekker, Inc., New York, 1995. MR 1352684
- M. I. Gil, A nonsingularity criterion for matrices, Linear Algebra Appl. 253 (1997), 79–87. MR 1431166, DOI 10.1016/0024-3795(95)00704-0
- Michael I. Gil′, Stability of finite- and infinite-dimensional systems, The Kluwer International Series in Engineering and Computer Science, vol. 455, Kluwer Academic Publishers, Boston, MA, 1998. MR 1666431, DOI 10.1007/978-1-4615-5575-9
- M. I. Gil′, Invertibility conditions and bounds for spectra of matrix integral operators, Monatsh. Math. 129 (2000), no. 1, 15–24. MR 1741036, DOI 10.1007/s006050050002
- M. I. Gil’, Invertibility and positive invertibility of integral operators in $L^\infty$, J. Integral Equations Appl. 13 (2001), no. 1, 1–14. MR 1827372, DOI 10.1216/jiea/996986880
- M. I. Gil′, On invertibility and positive invertibility of matrices, Linear Algebra Appl. 327 (2001), no. 1-3, 95–104. MR 1823342, DOI 10.1016/S0024-3795(00)00313-X
- I. C. Gohberg and M. G. Kreĭn, Theory and applications of Volterra operators in Hilbert space, Translations of Mathematical Monographs, Vol. 24, American Mathematical Society, Providence, R.I., 1970. Translated from the Russian by A. Feinstein. MR 0264447
- Hermann König, Eigenvalue distribution of compact operators, Operator Theory: Advances and Applications, vol. 16, Birkhäuser Verlag, Basel, 1986. MR 889455, DOI 10.1007/978-3-0348-6278-3
- M. A. Krasnosel′skij, Je. A. Lifshits, and A. V. Sobolev, Positive linear systems, Sigma Series in Applied Mathematics, vol. 5, Heldermann Verlag, Berlin, 1989. The method of positive operators; Translated from the Russian by Jürgen Appell. MR 1038527
- Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Inc., Boston, Mass., 1964. MR 0162808
- A. Pietsch, Eigenvalues and $s$-numbers, Mathematik und ihre Anwendungen in Physik und Technik [Mathematics and its Applications in Physics and Technology], vol. 43, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987. MR 917067
Additional Information
- M. I. Gil’
- Affiliation: Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
- Email: gilmi@black.bgu.ac.il
- Received by editor(s): March 21, 2001
- Received by editor(s) in revised form: June 24, 2002
- Published electronically: February 20, 2003
- Additional Notes: This research was supported by the Israel Ministry of Science and Technology
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3737-3746
- MSC (2000): Primary 47A55, 47A75; Secondary 47G10, 47G20
- DOI: https://doi.org/10.1090/S0002-9939-03-06950-8
- MathSciNet review: 1998181