Abstract
The size of the perturbation class {S∈L(E)∶S has closed range}+I(E) is studied, whereE is a Banach space andI(E) stands for various classical operator ideals. For instance, it is shown for the ideal consisting of the inessential operators that the resulting perturbation class does not exhaust the class of bounded linear operators under natural structural conditions onE. It is known from a recent result of Gowers and Maurey that some conditions are needed.
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