Daugavet Centers
An operator G: X → Y is said to be a Daugavet center if ||G + T|| = ||G|| + ||T|| for every rank-1 operator T: X → Y . The main result of the paper is: if G: X →! Y is a Daugavet center, Y is a subspace of a Banach space E, and J : Y → E is the natural embedding operator, then E can be equivalently...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106629 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Daugavet Centers / T. Bosenko, V. Kadets // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 3-20. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862682425855836160 |
|---|---|
| author | Bosenko, T. Kadets, V. |
| author_facet | Bosenko, T. Kadets, V. |
| citation_txt | Daugavet Centers / T. Bosenko, V. Kadets // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 3-20. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | An operator G: X → Y is said to be a Daugavet center if ||G + T|| = ||G|| + ||T|| for every rank-1 operator T: X → Y . The main result of the paper is: if G: X →! Y is a Daugavet center, Y is a subspace of a Banach space E, and J : Y → E is the natural embedding operator, then E can be equivalently renormed in such a way that J ○ G : X → E is also a Daugavet center. This result was previously known for the particular case X = Y, G = Id and only in separable spaces. The proof of our generalization is based on an idea completely di®erent from the original one. We also give some geometric characterizations of the Daugavet centers, present a number of examples, and generalize (mostly in straightforward manner) to Daugavet centers some results known previously for spaces with the Daugavet property.
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| first_indexed | 2025-12-07T15:52:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106629 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T15:52:42Z |
| publishDate | 2010 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Bosenko, T. Kadets, V. 2016-10-01T15:04:24Z 2016-10-01T15:04:24Z 2010 Daugavet Centers / T. Bosenko, V. Kadets // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 3-20. — Бібліогр.: 14 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106629 An operator G: X → Y is said to be a Daugavet center if ||G + T|| = ||G|| + ||T|| for every rank-1 operator T: X → Y . The main result of the paper is: if G: X →! Y is a Daugavet center, Y is a subspace of a Banach space E, and J : Y → E is the natural embedding operator, then E can be equivalently renormed in such a way that J ○ G : X → E is also a Daugavet center. This result was previously known for the particular case X = Y, G = Id and only in separable spaces. The proof of our generalization is based on an idea completely di®erent from the original one. We also give some geometric characterizations of the Daugavet centers, present a number of examples, and generalize (mostly in straightforward manner) to Daugavet centers some results known previously for spaces with the Daugavet property. Research of the second named author was conducted during his stay in the University of Granada and was supported by Junta de Andalucia grant P06-FQM-01438. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Daugavet Centers Article published earlier |
| spellingShingle | Daugavet Centers Bosenko, T. Kadets, V. |
| title | Daugavet Centers |
| title_full | Daugavet Centers |
| title_fullStr | Daugavet Centers |
| title_full_unstemmed | Daugavet Centers |
| title_short | Daugavet Centers |
| title_sort | daugavet centers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106629 |
| work_keys_str_mv | AT bosenkot daugavetcenters AT kadetsv daugavetcenters |