Daugavet centers are separably determined
A linear bounded operator $G$ acting from a~Banach space $X$ intoa~Banach space $Y$ is a~Daugavet center if every linear boundedrank-$1$ operator $Tcolon X o Y$ fulfills$|G+T|=|G|+|T|$. We prove that $G colon X o Y$is a~Daugavet center if and only if for every separable subspaces$X_1subset X$ and...
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| Main Author: | |
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| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2013-10-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/texts/2013/40_1/66-70.pdf |
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| Summary: | A linear bounded operator $G$ acting from a~Banach space $X$ intoa~Banach space $Y$ is a~Daugavet center if every linear boundedrank-$1$ operator $Tcolon X o Y$ fulfills$|G+T|=|G|+|T|$. We prove that $G colon X o Y$is a~Daugavet center if and only if for every separable subspaces$X_1subset X$ and $Y_1subset Y$ there exist separable subspaces$X_2subset X$ and $Y_2subset Y$ such that $X_1subset X_2$,$Y_1subset Y_2$, $G(X_2)subset Y_2$ and the restriction$G|_{X_2} colon X_2 o Y_2$ of $G$ is a~Daugavetcenter. We apply this fact to study the set of $G$-narrowoperators. |
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| ISSN: | 1027-4634 |