The oscillation of an operator on

Authors:
George R. Barnes and Robert Whitley

Journal:
Trans. Amer. Math. Soc. **211** (1975), 339-351

MSC:
Primary 47B37

DOI:
https://doi.org/10.1090/S0002-9947-1975-0405158-6

MathSciNet review:
0405158

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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce and discuss the oscillation of an operator *T* mapping 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 and a corresponding perturbation class which contains the compact operators.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0405158-6

Keywords:
Diffuse operator,
operator,
compact operator,
concentrated operator,
semi-Fredholm operator,
Fredholm operator,
perturbation theory

Article copyright:
© Copyright 1975
American Mathematical Society