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2010 Mathematics Subject Classification: 47A10.
We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.
The purpose of this work is to give a topological condition for the usual product of two closed operators acting in a Hilbert space to be closed.
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