On the topological boundary of semi-Fredholm operators
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- by Haïkel Skhiri PDF
- Proc. Amer. Math. Soc. 126 (1998), 1381-1389 Request permission
Abstract:
We prove several distance formulas from a fixed operator in $B(H)$ to some classes of operators connected with the semi-Fredholm ones. Here $H$ is a separable Hilbert space. In particular, Fredholm and upper and lower semi-Fredholm operators have the same boundary in $B(H)$.References
- Richard Bouldin, The essential minimum modulus, Indiana Univ. Math. J. 30 (1981), no. 4, 513–517. MR 620264, DOI 10.1512/iumj.1981.30.30042
- Richard Bouldin, Approximation by semi-Fredholm operators with fixed nullity, Rocky Mountain J. Math. 20 (1990), no. 1, 39–50. MR 1057973, DOI 10.1216/rmjm/1181073157
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- Saichi Izumino and Yoshinobu Kato, The closure of invertible operators on a Hilbert space, Acta Sci. Math. (Szeged) 49 (1985), no. 1-4, 321–327. MR 839947
- W. J. Trjitzinsky, General theory of singular integral equations with real kernels, Trans. Amer. Math. Soc. 46 (1939), 202–279. MR 92, DOI 10.1090/S0002-9947-1939-0000092-6
- Donald D. Rogers, Approximation by unitary and essentially unitary operators, Acta Sci. Math. (Szeged) 39 (1977), no. 1-2, 141–151. MR 448130
- Pei Yuan Wu, Approximation by invertible and noninvertible operators, J. Approx. Theory 56 (1989), no. 3, 267–276. MR 990341, DOI 10.1016/0021-9045(89)90116-0
Additional Information
- Haïkel Skhiri
- Affiliation: Département de Mathématiques, Bât. M2, Université de Lille I, F–59655 Villeneuve d’Ascq, France
- Email: skhiri@gat.univ-lille1.fr
- Received by editor(s): April 30, 1996
- Received by editor(s) in revised form: October 14, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1381-1389
- MSC (1991): Primary 47A53; Secondary 47A55
- DOI: https://doi.org/10.1090/S0002-9939-98-04262-2
- MathSciNet review: 1443858