R. Y. Yakymiv

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Articles: 2

On well-behaved representations of $\lambda$-deformed CCR

D. P. Proskurin, L. B. Turowska, R. Y. Yakymiv

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 23 (2017), no. 2, 192-205

We study well-behaved ∗-representations of a λ-deformation of Wick analog of CCR algebra. Homogeneous Wick ideals of degrees two and three are described. Well-behaved irreducible ∗-representations of quotients by these ideals are classified up to unitary equivalence.

Representations of relations with orthogonality condition and their deformations

V. L. Ostrovskyi, D. P. Proskurin, R. Y. Yakymiv

↓ Abstract   |   Article (.pdf)

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.

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