$\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$
UDC 517.5 It is shown that every $\varepsilon$-isometry of a convex body in $l^n_\infty$ or in $l^n_1$ can be well approximated by an affine surjective isometry.
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8295 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513019818147840 |
|---|---|
| author | Vestfrid, Igor A. Vestfrid, Igor A. |
| author_facet | Vestfrid, Igor A. Vestfrid, Igor A. |
| author_sort | Vestfrid, Igor A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-04-16T12:01:19Z |
| description | UDC 517.5
It is shown that every $\varepsilon$-isometry of a convex body in $l^n_\infty$ or in $l^n_1$ can be well approximated by an affine surjective isometry. |
| doi_str_mv | 10.3842/umzh.v76i9.8295 |
| first_indexed | 2026-03-24T03:38:02Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8295 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:02Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-82952025-04-16T12:01:19Z $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ Vestfrid, Igor A. Vestfrid, Igor A. \varepsilon--isometry, isometric approximation, classical Banach spaces, stability UDC 517.5 It is shown that every $\varepsilon$-isometry of a convex body in $l^n_\infty$ or in $l^n_1$ can be well approximated by an affine surjective isometry. УДК 517.5 $\varepsilon$-Изометрії опуклих тіл у $l^n_\infty$ і $l^n_1$ Показано, що кожна $\varepsilon$-ізометрія опуклого тіла в $l^n_\infty$ або в $l^n_1$ може бути ефективно наближена за допомогою афінної сюр'єктивної ізометрії. Institute of Mathematics, NAS of Ukraine 2025-04-16 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8295 10.3842/umzh.v76i9.8295 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 9 (2024); 1419 - 1423 Український математичний журнал; Том 76 № 9 (2024); 1419 - 1423 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8295/10171 Copyright (c) 2024 Igor A. Vestfrid |
| spellingShingle | Vestfrid, Igor A. Vestfrid, Igor A. $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title | $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title_alt | $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title_full | $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title_fullStr | $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title_full_unstemmed | $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title_short | $\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| title_sort | $\varepsilon$-isometries of convex bodies in $l^n_\infty$ and $l^n_1$ |
| topic_facet | \varepsilon--isometry isometric approximation classical Banach spaces stability |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8295 |
| work_keys_str_mv | AT vestfridigora varepsilonisometriesofconvexbodiesinlninftyandln1 AT vestfridigora varepsilonisometriesofconvexbodiesinlninftyandln1 |