D. Yu. Yakymenko

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Articles: 3

Decomposition of a unitary scalar operator into a product of roots of the identity

D. Yu. Yakymenko

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 19 (2013), no. 2, 191-196

We prove that for all $m_1,m_2,m_3 \in \mathbb{N},~ \frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3} \leq 1$, every unitary scalar operator $\gamma I$ on a complex infinite-dimensional Hilbert space is a product $\gamma I = U_1 U_2 U_3$ where $U_i$ is a unitary operator such that $U_i^{m_i} = I$.

Unitarization of Schur representations of a poset corresponding to $\widetilde{E_8}$

D. Yu. Yakymenko

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 16 (2010), no. 3, 264-270

We prove that every Schur representation of a poset corresponding to $\widetilde{E_8}$ can be unitarized with some character.

On $n$-tuples of subspaces in linear and unitary spaces

Yu. S. Samoilenko, D. Yu. Yakymenko

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 15 (2009), no. 1, 48-60

We study a relation between brick $n$-tuples of subspaces of a finite dimensional linear space, and irreducible $n$-tuples of subspaces of a finite dimensional Hilbert (unitary) space such that a linear combination, with positive coefficients, of orthogonal projections onto these subspaces equals the identity operator. We prove that brick systems of one-dimensional subspaces and the systems obtained from them by applying the Coxeter functors (in particular, all brick triples and quadruples of subspaces) can be unitarized. For each brick triple and quadruple of subspaces, we describe sets of characters that admit a unitarization.


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