The oscillation of an operator

Whitley, Robert

doi:10.1090/S0002-9947-1972-0295105-X

The oscillation of an operator
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Trans. Amer. Math. Soc. 165 (1972), 65-73 Request permission

Erratum: Trans. Amer. Math. Soc. 172 (1972), 507.

Abstract:

Foiaş and Singer introduced the oscillation of a bounded linear operator mapping $C(S)$ into a Banach space. Using this concept we define a generalization of the Fredholm operators T with $\mathcal {K}(T) < \infty$ and a corresponding perturbation class which contains the weakly compact operators. We show that a bounded linear operator on c is a conservative summability matrix which sums every bounded sequence if and only if it has zero oscillation at infinity.

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