Properties of restrictions of the operator of multiplication by a continuous function
For the operatorA of multiplication by a continuous functiona (t) in the Hilbert spaceL 2[0, b]=H, we give a description of two sets of infinite-dimensional subspaces with infinite codimensions:I(A)={N⊂H:A/N is an isomorphism},K(A)={M⊂H: A/M is a compact mapping}. As an application, we consider the...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5570 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511799871275008 |
|---|---|
| author | Shevchik, V. V. Шевчик, В. В. |
| author_facet | Shevchik, V. V. Шевчик, В. В. |
| author_sort | Shevchik, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:13:33Z |
| description | For the operatorA of multiplication by a continuous functiona (t) in the Hilbert spaceL 2[0, b]=H, we give a description of two sets of infinite-dimensional subspaces with infinite codimensions:I(A)={N⊂H:A/N is an isomorphism},K(A)={M⊂H: A/M is a compact mapping}. As an application, we consider the problem of determining whether the sequence {a(t)en(t)}, where {en(t)} is an orthonormal basis in L2[0,b], is an unconditional basis. |
| first_indexed | 2026-03-24T03:18:38Z |
| format | Article |
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| id | umjimathkievua-article-5570 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:18:38Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f0/c5412a0f27c3fa2c02ac4ec1d3b8c8f0.pdf |
| spelling | umjimathkievua-article-55702020-03-19T09:13:33Z Properties of restrictions of the operator of multiplication by a continuous function Properties of restrictions of the operator of multiplication by a continuous function Shevchik, V. V. Шевчик, В. В. For the operatorA of multiplication by a continuous functiona (t) in the Hilbert spaceL 2[0, b]=H, we give a description of two sets of infinite-dimensional subspaces with infinite codimensions:I(A)={N⊂H:A/N is an isomorphism},K(A)={M⊂H: A/M is a compact mapping}. As an application, we consider the problem of determining whether the sequence {a(t)en(t)}, where {en(t)} is an orthonormal basis in L2[0,b], is an unconditional basis. Для оператора $А$ множення на неперервну функцію $a (t)$ в просторі $L_2[0, b] =H,$ дано опис двох множин нескінченновимірних підпросторів нескінченної корозмірності: $I(A) = \{N ⊂ H: A/N$ — ізоморфізм $\}$, $K(A) = \{M ⊂ H: A/M$ — компактне відображення$\}$. Як приклад розглянуто питання про безумовну базисність послідовності $\{a(t)e_n(t)\}, $, де ${e_n(t)}$ — ортонормована послідовність в $L_2[0,b]$. Institute of Mathematics, NAS of Ukraine 1995-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5570 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 12 (1995); 1720–1722 Український математичний журнал; Том 47 № 12 (1995); 1720–1722 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5570/7827 https://umj.imath.kiev.ua/index.php/umj/article/view/5570/7828 Copyright (c) 1995 Shevchik V. V. |
| spellingShingle | Shevchik, V. V. Шевчик, В. В. Properties of restrictions of the operator of multiplication by a continuous function |
| title | Properties of restrictions of the operator of multiplication by a continuous function |
| title_alt | Properties of restrictions of the operator of multiplication by a continuous function |
| title_full | Properties of restrictions of the operator of multiplication by a continuous function |
| title_fullStr | Properties of restrictions of the operator of multiplication by a continuous function |
| title_full_unstemmed | Properties of restrictions of the operator of multiplication by a continuous function |
| title_short | Properties of restrictions of the operator of multiplication by a continuous function |
| title_sort | properties of restrictions of the operator of multiplication by a continuous function |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5570 |
| work_keys_str_mv | AT shevchikvv propertiesofrestrictionsoftheoperatorofmultiplicationbyacontinuousfunction AT ševčikvv propertiesofrestrictionsoftheoperatorofmultiplicationbyacontinuousfunction |