The oscillation of an operator on 𝐿^{𝑝}

Barnes, George R.; Whitley, Robert

doi:10.1090/S0002-9947-1975-0405158-6

The oscillation of an operator on $L^{p}$
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by George R. Barnes and Robert Whitley PDF

Trans. Amer. Math. Soc. 211 (1975), 339-351 Request permission

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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