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

2020/02/20 by Marat V. Markin, Markin, Marat V.
Mathematics · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2002.09087

Abstract

We establish spectral inclusion and mapping theorems for scalar type spectral\noperators, generalizing their counterparts for normal operators. Thereby, we\nextend a precise weak spectral mapping theorem, known to hold for\nC₀-semigroups of normal operators on complex Hilbert spaces, to the more\ngeneral case of C₀-semigroups of scalar type spectral operators on complex\nBanach spaces. The finer spectrum structure is given itemized consideration.\n

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