On Sums of Projections

S. A. Kruglyak ; V. I. Rabanovich ; Yu. S. Samoilenko

Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 20-35.

Résumé

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 $\alpha\in\Sigma_n$.

Détail

Keywords: algebra, representation, operator, projection, identity.
Mots-clés : matrix

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