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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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2010
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106629 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Daugavet Centers / T. Bosenko, V. Kadets // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 3-20. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106629 |
|---|---|
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dspace |
| spelling |
irk-123456789-1066292016-10-02T03:02:41Z Daugavet Centers Bosenko, T. Kadets, V. 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. 2010 Article Daugavet Centers / T. Bosenko, V. Kadets // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 3-20. — Бібліогр.: 14 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106629 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bosenko, T. Kadets, V. |
| spellingShingle |
Bosenko, T. Kadets, V. Daugavet Centers Журнал математической физики, анализа, геометрии |
| author_facet |
Bosenko, T. Kadets, V. |
| author_sort |
Bosenko, T. |
| title |
Daugavet Centers |
| title_short |
Daugavet Centers |
| title_full |
Daugavet Centers |
| title_fullStr |
Daugavet Centers |
| title_full_unstemmed |
Daugavet Centers |
| title_sort |
daugavet centers |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106629 |
| citation_txt |
Daugavet Centers / T. Bosenko, V. Kadets // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 3-20. — Бібліогр.: 14 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT bosenkot daugavetcenters AT kadetsv daugavetcenters |
| first_indexed |
2023-10-18T20:13:21Z |
| last_indexed |
2023-10-18T20:13:21Z |
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1796149294248493056 |