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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The oscillation of an operator


Author: Robert Whitley
Journal: Trans. Amer. Math. Soc. 165 (1972), 65-73
MSC: Primary 47A99; Secondary 40J05
DOI: https://doi.org/10.1090/S0002-9947-1972-0295105-X
Erratum: Trans. Amer. Math. Soc. 172 (1972), 507.
MathSciNet review: 0295105
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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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DOI: https://doi.org/10.1090/S0002-9947-1972-0295105-X
Keywords: Bounded linear operator on $ C(S)$, oscillation of an operator, Fredholm operator, ramming operator, weakly compact operator, strictly singular operator, $ {\varphi _ + }$ operator, conservative summability method, coercive summability method
Article copyright: © Copyright 1972 American Mathematical Society