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

الأصل · EN

Let (P₁,...,Pₙ) be an n--tuple of projections in a unital C*--algebra å. We say is complete in å if å is the linear direct sum of the closed subspaces P₁å,...,Pₙå. In this paper, we give some necessary and sufficient conditions for the completeness of 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.