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Transactions of the American Mathematical Society

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



The oscillation of an operator on $ L\sp{p}$

Authors: George R. Barnes and Robert Whitley
Journal: Trans. Amer. Math. Soc. 211 (1975), 339-351
MSC: Primary 47B37
MathSciNet review: 0405158
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Abstract: We introduce and discuss the oscillation of an operator T mapping $ {L^p}(S,\Sigma ,\mu )$ into a Banach space. We establish results relating the oscillation, a ``local norm", to the norm of the operator. Also using the oscillation we define a generalization of the Fredholm operators T with index $ \kappa (T) < \infty $ and a corresponding perturbation class which contains the compact operators.

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Keywords: Diffuse operator, $ {c_0}$ operator, compact operator, concentrated operator, semi-Fredholm operator, Fredholm operator, perturbation theory
Article copyright: © Copyright 1975 American Mathematical Society