On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913127535214592 |
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| author | Markin, Marat V. |
| author_facet | Markin, Marat V. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_09087 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups Markin, Marat V. Functional Analysis Spectral Theory Primary 47A10, 47B40, 47D03, Secondary 47B15, 47D06, 47D60 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. |
| title | On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups |
| topic | Functional Analysis Spectral Theory Primary 47A10, 47B40, 47D03, Secondary 47B15, 47D06, 47D60 |
| url | https://arxiv.org/abs/2002.09087 |