, Volume 36, Issue 3, pp 182-195

On Sums of Projections

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In the paper, for all n∈ℕ, we describe the set ∑n of all real numbers α admitting a collection of projections P 1,...,P n on a Hilbert space H such that ∑k=1 n P kI (I is the identity operator on H) and study the problem to find all collections of this kind for a given α∈∑ n .