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Supertauberian operators and perturbations.

M. González, A. Martínez-Abejón (1993)

Extracta Mathematicae

Upper semi-Fredholm operators and tauberian operators in Banach spaces admit the following perturbative characterizations [6], [2]: An operator T: X --> Y is upper semi-Fredholm (tauberian) if and only if for every compact operator K: X --> Y the kernel N(T+K) is finite dimensional (reflexive). In [7] Tacon introduces an intermediate class between upper semi-Fredholm operators and tauberian operators, the supertauberian operators, and he studies this class using non-standard analysis....

Sur la conorme essentielle

Mostafa Mbekhta, Rodolphe Paul (1996)

Studia Mathematica

Pour un opérateur T borné sur un espace de Hilbert dans lui-même, nous montrons que γ ( π ( T ) ) = s u p γ ( T + K ) : K o p é r a t e u r c o m p a c t , 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)).

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