Geodesic
On Sums of Projections
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 20-35

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In the paper, for all $n\in\mathbb{N}$, we describe the set $\Sigma_n$ of all real numbers $\alpha$ admitting a collection of projections $P_1,\dots,P_n$ on a Hilbert space $H$ such that $\sum_{k=1}^n P_k=\alpha I$ ($I$ is the identity operator on $H$) and study the problem to find all collections of this kind for a given $\alpha\in\Sigma_n$.
Keywords: algebra, representation, operator, projection, identity.
Mots-clés : matrix 
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S. A. Kruglyak; V. I. Rabanovich; Yu. S. Samoilenko. On Sums of Projections. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 20-35. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a2/