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Sep 28, 2019 at 23:02 comment added sbisaf Thanks @user131781. I agree I didn't express precisely my question. I actually had in mind what you suggest as point 1). The main point was to understand what can be said about the behavior of the operator in the subspace to which the eigenvectors do not belong. I was wondering for which class of operators the property of vanishing on that subspace holds, if it is wider than the class of compact normal operators of not. Your answer was valuable to me.
Sep 27, 2019 at 9:25 history answered user131781 CC BY-SA 4.0