Semi-Fredholm operators with finite ascent or descent and perturbations

Rakočević, Vladimir

doi:10.1090/S0002-9939-1995-1286004-6

Semi-Fredholm operators with finite ascent or descent and perturbations
HTML articles powered by AMS MathViewer

by Vladimir Rakočević PDF

Proc. Amer. Math. Soc. 123 (1995), 3823-3825 Request permission

Abstract:

In this note we prove that the collection of upper (lower) semi-Fredholm operators with finite ascent (descent) is closed under commuting operator perturbations that belong to the perturbation class associated with the set of upper (lower) semi-Fredholm operators. Then, as a corollary we get the main result of S. Grabiner (Proc. Amer. Math. Soc. 71 (1978), 79-80).

References

S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 9, Marcel Dekker, Inc., New York, 1974. MR 0415345
M. A. Gol′dman and S. N. Kračkovskiĭ, Behavior of the space of zeros with a finite-dimensional salient on the Riesz kernel under perturbations of the operator, Dokl. Akad. Nauk SSSR 221 (1975), no. 13, 532–534 (Russian). MR 0477829
Sandy Grabiner, Ascent, descent and compact perturbations, Proc. Amer. Math. Soc. 71 (1978), no. 1, 79–80. MR 495841, DOI 10.1090/S0002-9939-1978-0495841-7
Robin Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR 920812
Vladimir Rakočević, Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), no. 2, 193–198. MR 848425, DOI 10.1017/S0017089500006509
T. T. West, A Riesz-Schauder theorem for semi-Fredholm operators, Proc. Roy. Irish Acad. Sect. A 87 (1987), no. 2, 137–146. MR 941708
Jaroslav Zemánek, Compressions and the Weyl-Browder spectra, Proc. Roy. Irish Acad. Sect. A 86 (1986), no. 1, 57–62. MR 865103