| Autor: |
Daptari, Soumitra, Paul, Tanmoy, Rao, T. S. S. R. K. |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Linear and Multilinear Algebra 2021 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1080/03081087.2021.1945526 |
| Popis: |
In this paper we study two properties viz. property-$U$ and property-$SU$ of a subspace $Y$ of a Banach space which correspond to the uniqueness of the Hahn-Banach extension of each linear functional in $Y^*$ and in addition to that this association forms a linear operator of norm-1 from $Y^*$ to $X^*$. It is proved that, under certain geometric assumptions on $X, Y, Z$ these properties are stable with respect to the injective tensor product; $Y$ has property-$U$ ($SU$) in $Z$ if and only if $X\otimes_\e^\vee Y$ has property-$U$ ($SU$) in $X\otimes_\e^\vee Z$. We prove that when $X^*$ has the Radon-Nikod$\acute{y}$m Property for $13$ is a Hilbert space if and only if for any two subspaces $Y, Z$ with property-$SU$ in $X$, $Y+Z$ has property-$SU$ in $X$ whenever $Y+Z$ is closed. We characterize all hyperplanes in $c_0$ which have property-$SU$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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