Sur la conorme essentielle
Mbekhta, Mostafa ; Paul, Rodolphe
Studia Mathematica, Tome 119 (1996), p. 243-252 / Harvested from The Polish Digital Mathematics Library

Pour un opérateur T borné sur un espace de Hilbert dans lui-même, nous montrons que γ(π(T))=supγ(T+K):Kopérateurcompact, où γ est la conorme (the reduced minimum modulus) et π(T) est la classe de T dans l’algèbre de Calkin. Nous montrons aussi que ce supremum est atteint. D’autre part, nous montrons que les opérateurs semi-Fredholm caractérisent les points de continuité de l’application T → γ (π(T)).

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216254
@article{bwmeta1.element.bwnjournal-article-smv117i3p243bwm,
     author = {Mostafa Mbekhta and Rodolphe Paul},
     title = {Sur la conorme essentielle},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {243-252},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p243bwm}
}
Mbekhta, Mostafa; Paul, Rodolphe. Sur la conorme essentielle. Studia Mathematica, Tome 119 (1996) pp. 243-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p243bwm/

[00000] [1] C. A. Akemann and G. K. Pedersen, Ideal perturbations of elements in C*-algebras, Math Scand. 41 (1977), 117-139. | Zbl 0377.46049

[00001] [2] C. Apostol, The reduced minimum modulus, Michigan Math. J. 32 (1985), 279-294. | Zbl 0613.47008

[00002] [3] K. Astala and H.-O. Tylli, On the bounded compact approximation property and measures of noncompactness, J. Funct. Anal. 70 (1987), 388-401. | Zbl 0614.46011

[00003] [4] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966. | Zbl 0148.12501

[00004] [5] P. R. Halmos, A Hilbert Space Problem Book, D. Van Nostrand, 1967.

[00005] [6] P. de la Harpe, Initiation à l'algèbre de Calkin, in: Lecture Notes in Math. 725, Springer, 1978, 180-219.

[00006] [7] R. E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103 (1992), 71-77. | Zbl 0810.46062

[00007] [8] R. E. Harte and M. Mbekhta, Generalized inverses in C*-algebras II, ibid. 106 (1993), 129-138. | Zbl 0810.46063

[00008] [9] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.

[00009] [10] J. Ph. Labrousse et M. Mbekhta, Les opérateurs points de continuité pour la conorme et l'inverse de Moore-Penrose, Houston J. Math. 18 (1992), 7-23.

[00010] [11] L. E. Labuschagne, A. Ströh and J. Swart, The uniqueness of operational quantities in von Neumann algebras, preprint. | Zbl 0826.46048

[00011] [12] C. L. Olsen and J. K. Plastiras, Quasialgebraic operators, compact perturbations, and the essential norm, Michigan Math. J. 21 (1974), 385-397. | Zbl 0312.47016

[00012] [13] G. K. Pedersen, Spectral formulas in quotient C*-algebras, Math. Z. 148 (1976), 299-300. | Zbl 0319.46042

[00013] [14] J. Zemánek, Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219-234. | Zbl 0556.47008

[00014] [15] J. Zemánek, The semi-Fredholm radius of a linear operator, Bull. Polish Acad. Sci. Math. 32 (1984), 67-76. | Zbl 0583.47016