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

2012/10/17 by Shanwen Hu, Hu, Shanwen, Yifeng Xue +1 · 1 citation
Mathematics · Physics and Astronomy · #46L05 #47B65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1210.4670

openalex publication_date 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (P₁,...,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 P₁å,...,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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