Completeness of $n$--tuple of projections in $C^{\ast }$--algebras

Abstract

Let $(P_1,...,P_n)$ be an $n$--tuple of projections in a unital $C^{\ast }$--algebra $\mathring{a}$. We say $\pn$ is complete in $\mathring{a}$ if $\mathring{a}$ is the linear direct sum of the closed subspaces $P_1\mathring{a},...,P_n\mathring{a}$. 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 $\mathring{a}$. Some interesting and significant results are obtained in this paper.

21 pages

Cited by in corpus (2)

• Least Squares Problems in Orthornormalization
• $C^{\ast }$-algebras generated by three projections