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| SOME PROPERTIES OF THE $\[{l_2}\]$-VALUED LONGJAMES BANACH SPACE $\[J(\eta ,{l_2})\]$ |
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Citation： |
Zhao Junfeng.SOME PROPERTIES OF THE $\[{l_2}\]$-VALUED LONGJAMES BANACH SPACE $\[J(\eta ,{l_2})\]$[J].Chinese Annals of Mathematics B,1987,8(4):401~407 |
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Net amount： 790 |
Authors： |
Zhao Junfeng; |
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| Abstract： |
The main result of this paper is to show that the bidual $\[J(\eta ,{l_2})\]$ of the long James type $\[{l_2}\]$-valued Banach, space $\[J(\eta ,{l_2})\]$ can be identified with transfinite matrices of scalars
$\[{[({b_{a,i}})i \in [0,\omega )]_{a \in [0,\eta )}}\]$ with some conditions and the norm of the element x** in $\[J(\eta ,{l_2})\]$** equals $\[\mathop {\sup }\limits_{\gamma \in [0,\eta )} {\left\| {\sum\limits_{\alpha \in [0,\gamma )} {\sum\limits_{i \in [0,\omega )} {{b_{a,i}}{\phi _{a,i}}} } } \right\|_{J{{(\eta ,l)}^{**}}}}\]$. |
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