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http://hdl.handle.net/10662/12288
Title: | Invariant subspace problem and compact operators on non-Archimedean Banach spaces |
Authors: | Babahmed, M. El Asri, A. |
Keywords: | Invariant subspace;Hyperinvariant subspace;Compact operator;t-orthogonal basis;Quasi null vector;Triangular operator;Shift operator;Subespacio invariante;Subespacio hiperinvariante;Operador compacto;Base t-ortogonal;Vector cuasi nulo;Operador triangular;Operador de cambio |
Issue Date: | 2020 |
Publisher: | Universidad de Extremadura |
Abstract: | In this paper, the invariant Subspace Problem is studied for the class of non-Archimedean compact operators on an infinite-dimensional Banach space E over a nontrivial complete non-Archimedean valued field K. Our first main result (Theorem 9) asserts that if K is locally compact, then each compact operator on E possessing a quasi null vector admits a nontrivial hyperinvariant closed subspace. In the second one (Theorem 17), we prove that each bounded operator on E which contains a cyclic quasi null vector can be written as the sum of a triangular operator and a compact shift operator, each one of them possesses a nontrivial invariant closed subspace. Finally, we conclude that if K is algebraically closed, then every compact operator on E either has a nontrivial invariant closed subspace or is a sum of upper triangular operator and shift operator, each of them is compact and has a nontrivial invariant closed subspace. |
URI: | http://hdl.handle.net/10662/12288 |
DOI: | 10.17398/2605-5686.35.2.205 |
Appears in Collections: | Extracta Mathematicae Vol. 35, nº 2 (2020) |
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2605-5686_35_2_205.pdf | 396,75 kB | Adobe PDF | View/Open |
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