V. L. Ostrovskyi

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Articles: 7

Some remarks on Hilbert representations of posets

Methods Funct. Anal. Topology 20 (2014), no. 2, 149–163

For a certain class of finite posets, we prove that all their irreducible orthoscalar representations are finite-dimensional and describe those, for which there exist essential (non-degenerate) irreducible orthoscalar representations.

Representations of relations with orthogonality condition and their deformations

Methods Funct. Anal. Topology 18 (2012), no. 4, 373-386

Irreducible representations of $*$-algebras $A_q$ generated by relations of the form $a_i^*a_i+a_ia_i^*=1$, $i=1,2$, $a_1^*a_2=qa_2a_1^*$, where $q\in (0,1)$ is fixed, are classified up to the unitary equivalence. The case $q=0$ is considered separately. It is shown that the $C^*$-algebras $\mathcal{A}_q^F$ and $\mathcal{A}_0^F$ generated by operators of Fock representations of $A_q$ and $A_0$ are isomorphic for any $q\in (0,1)$. A realisation of the universal $C^*$-algebra $\mathcal{A}_0$ generated by $A_0$ as an algebra of continuous operator-valued functions is given.

On quadruples of linearly connected projections and transitive systems of subspaces

Methods Funct. Anal. Topology 13 (2007), no. 1, 43-49

We study conditions under which the images of irreducible quadruples of linearly connected projections give rise to all transitive systems of subspaces in a finite dimensional Hilbert space.

On $*$-representations of a certain class of algebras related to a graph

Vasyl Ostrovskyi

Methods Funct. Anal. Topology 11 (2005), no. 3, 250-256

Centered one-parameter semigroups

Vasyl Ostrovskyi

Methods Funct. Anal. Topology 10 (2004), no. 2, 32-42

On double commutator relation

Vasyl Ostrovskyĭ

Methods Funct. Anal. Topology 6 (2000), no. 2, 60-65

On operator relations, centered operators, and nonbijective dynamical systems

Vasyl’ Ostrovs’kyj

Methods Funct. Anal. Topology 2 (1996), no. 3, 114-121