A characterization of the Weyl spectrum
HTML articles powered by AMS MathViewer
- by Andrzej Pokrzywa PDF
- Proc. Amer. Math. Soc. 92 (1984), 215-218 Request permission
Abstract:
It is shown that for each closed subset $\Omega$ of the semi-Fredholm domain of a bounded linear operator $T$ acting in a complex Hilbert space $H$ there exists a subspace of a finite codimension in $H$ such that the compression of $T - \lambda$ to this subspace is a left- or right-invertible operator for all $\lambda$ in $\Omega$. From this result we obtain a characterization of the Weyl spectrum of $T$.References
- Constantin Apostol, The correction by compact perturbation of the singular behavior of operators, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 2, 155–175. MR 487559
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- Norberto Salinas, A characterization of the Browder spectrum, Proc. Amer. Math. Soc. 38 (1973), 369–373. MR 313852, DOI 10.1090/S0002-9939-1973-0313852-4 K. Gustafson, The Weyl-Browder algebraic essential spectrum and the Weinstein-Aronszajn determinant theory, Notices Amer. Math. Soc. 22 (1975), A709.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 215-218
- MSC: Primary 47A53; Secondary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0754706-6
- MathSciNet review: 754706