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
Date:2010
Main Authors: Bosenko, T., Kadets, V.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2010
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
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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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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