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arXiv · 2002.09087

On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups

Marat V. Markin
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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 $C_0$-semigroups of normal operators on complex Hilbert spaces, to the more general case of $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. The finer spectrum structure is given itemized consideration.

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Marat V. Markin. 2020-02-21. On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups. https://arxiv.org/abs/2002.09087

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