# A. V. Strelets

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### On the graph $K_{1,n}$ related configurations of subspaces of a Hilbert space

MFAT **23** (2017), no. 3, 285-300

285-300

We study systems of subspaces $H_1,\dots,H_N$ of a complex Hilbert space H that satisfy the following conditions: for every index $k > 1$, the set $\{\theta_{k,1},\ldots,\theta_{k,m_k}\}$ of angles $\theta_{k,i}\in(0,\pi/2)$ between $H_1$ and $H_k$ is fixed; all other pairs $H_k$, $H_j$ are orthogonal. The main tool in the study is a construction of a system of subspaces of a Hilbert space on the basis of its Gram operator (the G-construction).

### On *-representations of a class of algebras with polynomial growth related to Coxeter graphs

MFAT **17** (2011), no. 3, 252-273

252-273

For a Hilbert space $H$, we study configurations of its subspaces related to Coxeter graphs $\mathbb{G}_{s_1,s_2}$, $s_1,s_2\in\{4,5\}$, which are arbitrary trees such that one edge has type~$s_1$, another one has type~$s_2$ and the rest are of type~$3$. We prove that such irreducible configurations exist only in a finite dimensional $H$, where the dimension of $H$ does not exceed the number of vertices of the graph by more than twice. We give a description of all irreducible nonequivalent configurations; they are indexed with a continuous parameter. As an example, we study irreducible configurations related to a graph that consists of three vertices and two edges of type $s_1$ and $s_2$.

### On identities in the algebra generated by three partial reflections sum of which is zero

MFAT **10** (2004), no. 2, 86-90

86-90

### On "good" vectors for family of unbounded operators and their application

Yu. S. Samoĭlenko, A. V. Strelets

MFAT **8** (2002), no. 2, 88-100

88-100

### On a O*-representable algebras

MFAT **7** (2001), no. 4, 6-10

6-10