2019
Том 71
№ 1

# Yusenko A. A.

Articles: 2
Article (Ukrainian)

### Quadruples of orthoprojectors connected by a linear relationship

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 255–264

In the explicit form, we deduce formulas for all quadruples of orthoprojectors $P_1, P_2, P_3$, and $P_4$ irreducible to within unitary equivalence and connected by the linear relationship $α_1 P_1 + α_2 P_2 + α_3 P_3 + α_4 P_4 = λ I$, where $(α_1, α_2, α_3, α_4) ∈ ℝ^{+}$.

Article (Ukrainian)

### Quintuplets of orthoprojectors associated by a linear relation

Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 701-710

We consider the equation $α_1 P_1 + α_2 P_2 + … α_n P_n = I$ over orthoprojectors $P_1, … ,P_n$ in a Hilbert space. We show that the set of real parameters $(α_1, … α_n)$ for which there exists a solution of this equation in orthoprojectors contains an open set from $ℝ^5$.