Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators
The paper describes approximations properties of monotonically increasing sequences of invariant subspaces of a self-adjoint operator, as well as their symmetric generalizations in a complex Hilbert space, generated by its positive powers. It is established that the operator keeps its spectrum over...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/11/1918 |
| _version_ | 1797547196153856000 |
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| author | Oleh Lopushansky Renata Tłuczek-Piȩciak |
| author_facet | Oleh Lopushansky Renata Tłuczek-Piȩciak |
| author_sort | Oleh Lopushansky |
| collection | DOAJ |
| description | The paper describes approximations properties of monotonically increasing sequences of invariant subspaces of a self-adjoint operator, as well as their symmetric generalizations in a complex Hilbert space, generated by its positive powers. It is established that the operator keeps its spectrum over the dense union of these subspaces, equipped with quasi-norms, and that it is contractive. The main result is an inequality that provides an accurate estimate of errors for the best approximations in Hilbert spaces by these invariant subspaces. |
| first_indexed | 2024-03-10T14:40:53Z |
| format | Article |
| id | doaj.art-4b7565a2f4174ca2941a2c8f2c87ab14 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:40:53Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4b7565a2f4174ca2941a2c8f2c87ab142023-11-20T21:47:12ZengMDPI AGSymmetry2073-89942020-11-011211191810.3390/sym12111918Best Approximations by Increasing Invariant Subspaces of Self-Adjoint OperatorsOleh Lopushansky0Renata Tłuczek-Piȩciak1Institute of Mathematics, University of Rzeszów, 35-310 Rzeszów, PolandInstitute of Mathematics, University of Rzeszów, 35-310 Rzeszów, PolandThe paper describes approximations properties of monotonically increasing sequences of invariant subspaces of a self-adjoint operator, as well as their symmetric generalizations in a complex Hilbert space, generated by its positive powers. It is established that the operator keeps its spectrum over the dense union of these subspaces, equipped with quasi-norms, and that it is contractive. The main result is an inequality that provides an accurate estimate of errors for the best approximations in Hilbert spaces by these invariant subspaces.https://www.mdpi.com/2073-8994/12/11/1918spectral approximationexact errors estimationsself-adjoint operator |
| spellingShingle | Oleh Lopushansky Renata Tłuczek-Piȩciak Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators Symmetry spectral approximation exact errors estimations self-adjoint operator |
| title | Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators |
| title_full | Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators |
| title_fullStr | Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators |
| title_full_unstemmed | Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators |
| title_short | Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators |
| title_sort | best approximations by increasing invariant subspaces of self adjoint operators |
| topic | spectral approximation exact errors estimations self-adjoint operator |
| url | https://www.mdpi.com/2073-8994/12/11/1918 |
| work_keys_str_mv | AT olehlopushansky bestapproximationsbyincreasinginvariantsubspacesofselfadjointoperators AT renatatłuczekpieciak bestapproximationsbyincreasinginvariantsubspacesofselfadjointoperators |