We consider the equation α1 P 1 + α2 P 2 + … α n P n = I over orthoprojectors P 1, … ,P n in a Hilbert space. We show that the set of real parameters (α1, … α n ) for which there exists a solution of this equation in orthoprojectors contains an open set from ℝ5.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 5, pp. 701–710, May, 2009.
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Yusenko, A.A. Quintuplets of orthoprojectors associated by a linear relation. Ukr Math J 61, 834–846 (2009). https://doi.org/10.1007/s11253-009-0240-y
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DOI: https://doi.org/10.1007/s11253-009-0240-y