Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the topological boundary
of semi-Fredholm operators


Author: Haïkel Skhiri
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] R. Bouldin, The essential minimum modulus, Indiana. Univ. Math. J. 30 (1981), 513-517. MR 82i:47001
  • [2] R. Bouldin, Approximation by semi-Fredholm operators with fixed nullity, Rocky Mountain J. Math. 20 (1990), 39-50. MR 91m:47021
  • [3] P.R. Halmos, A Hilbert space problem book, D. Van Nostrand, 1967. MR 34:8178
  • [4] S. Izumino & Y. Kato, The closure of invertible operators on a Hilbert space, Acta. Sci. Math. (Szeged) 49 (1985), 321-327. MR 87h:47101
  • [5] M. Mbekhta, Sur la structure des composantes connexes semi-Fredholm de $B(H)$, Proc. Amer. Math. Soc. 116 (1992), 521-524. MR 92m:47021
  • [6] D.D. Rogers, Approximation by unitary and essentially unitary operators, Acta. Sci. Math. (Szeged) 39 (1977), 141-151. MR 56:6439
  • [7] P. Y. Wu, Approximation by invertible and noninvertible operators, J. Approx. Theory, 56 (1989), 267-276. MR 90c:47003

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A53, 47A55

Retrieve articles in all journals with MSC (1991): 47A53, 47A55


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

DOI: https://doi.org/10.1090/S0002-9939-98-04262-2
Keywords: Hilbert space operators, semi-Fredholm operators, distance formulas
Received by editor(s): April 30, 1996
Received by editor(s) in revised form: October 14, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society