On the normality of the sum of two normal operators
MH Mortad - Complex Analysis and Operator Theory, 2012 - Springer
Complex Analysis and Operator Theory, 2012•Springer
… Probably due to the complexity of the question, not much was done for perturbed normal
operators (we mention the references [1,12,13] where some perturbation of normal
operators was dealt with, in a very different context though). So in the present paper we
study perturbed normal operators and the main question asked here is: when is the sum of
two normal operators normal? We answer this question and we establish the normality of A
+ B (for normal A and B) in three settings, that is for …
operators (we mention the references [1,12,13] where some perturbation of normal
operators was dealt with, in a very different context though). So in the present paper we
study perturbed normal operators and the main question asked here is: when is the sum of
two normal operators normal? We answer this question and we establish the normality of A
+ B (for normal A and B) in three settings, that is for …
Abstract
The aim of this paper is to give sufficient conditions on two normal operators (bounded or not), defined on a Hilbert space, which make their algebraic sum normal. The results are accompanied by some interesting examples and counter examples.
Springer
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