On the hereditary character of certain spectral properties and some applications
Abstract In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that Tn(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove t...
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| Main Authors: | , , , , |
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| Language: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2021
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| Subjects: | |
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000501053 |
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| Summary: | Abstract In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that Tn(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semi-Fredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces. |
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