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1. Reflexivity and reducibility of operators related to invariant subspace problem | |||
Ji You Qing,Xu Xinjun | |||
Mathematics 07 January 2009 | |||
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Abstract:The well-known invariant subspace problem is A long-standing problem in operator theory,which has been to determine whether every (bounded linear) operator $T$ on a Banach space $X$ must have a nontrivial invariant subspace. every reducible subspace of $T$ is invariant subspace of $T$ too. We show that, for some Banach space operators $T$,( {\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it bi-crystal} operator) the following statements are equivalent. (1) There exists a nontrivial invariant subspace of $T$. (2) $T$ is Banach reducible. (3) $T$ is reflexive. And we show that if $A\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\sim A \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\bigoplus A$, then $A$ is reflexive. | |||
TO cite this article:Ji You Qing,Xu Xinjun. Reflexivity and reducibility of operators related to invariant subspace problem[OL].[ 7 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27437 |
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