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arXiv · 1210.4670

Completeness of $n$--tuple of projections in $C^*$--algebras

Shanwen Hu·Yifeng Xue
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Abstract

Let $(P_1,...,P_n)$ be an $n$--tuple of projections in a unital $C^*$--algebra $å$. We say $\pn$ is complete in $å$ if $å$ is the linear direct sum of the closed subspaces $P_1å,...,P_nå$. In this paper, we give some necessary and sufficient conditions for the completeness of $\pn$ and discuss the perturbation problem and topology of the set of all complete $n$--tuple of projections in $å$. Some interesting and significant results are obtained in this paper.

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Shanwen Hu, Yifeng Xue. 2012-10-17. Completeness of $n$--tuple of projections in $C^*$--algebras. https://arxiv.org/abs/1210.4670

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