On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups
Abstract
We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for C0-semigroups of normal operators on complex Hilbert spaces, to the more general case of C0-semigroups of scalar type spectral operators on complex Banach spaces. The finer spectrum structure is given itemized consideration.
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