2019
Том 71
№ 11

# Yakymenko D. Yu.

Articles: 4
Article (Russian)

### Scalar operators equal to the product of unitary roots of the identity operator

Ukr. Mat. Zh. - 2012. - 64, № 6. - pp. 819-825

We study the set of all $\gamma \in \mathbb{C}$ for which there exist unitary operators $U_i$ such that $U_1U_2 ... U_n = \gamma I$ and $U_i^{m_i} = I$, where $m_i \in \mathbb{N}$ are given.

Article (Russian)

### Unitarization of Schur representations of a partially ordered set associated with $\widetilde{E}_7$

Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 847–853

We prove that every Schur representation of a partially ordered set associated with graph $\widetilde{E}_7$ can be unitarized with some character.

Article (Russian)

### Unitarization of representations of a partially ordered set associated with a graph $\tilde{E}_6$

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1424-1433

It is shown that any Schur representation of a poset associated with a graph $\tilde{E}_6$ can be unitarized with a certain character. The description of characters for which it is possible to unitarize the Schur representations of $\tilde{E}_6$ is presented.

Article (Ukrainian)

### On indecomposable and transitive systems of subspaces

Ukr. Mat. Zh. - 2007. - 59, № 5. - pp. 717–720

We prove that the indecomposability of a system of subspaces of a finite-dimensional Hilbert space implies the transitivity of this system under the condition of the linear coherence of the corresponding system of orthogonal projectors.