Vasyl Ostrovskyi
@imath.kiev.ua
Institue of Mathematics, NAS of Ukraine
7
Scopus Publications
148
Scholar Citations
3
Scholar h-index
4
Scholar i10-index
Scopus Publications
- On families of twisted power partial isometries
V.L. Ostrovskyi, D.P. Proskurin, and R.Ya. Yakymiv
Vasyl Stefanyk Precarpathian National University
We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\\lambda_{ij}\\in\\mathbb C$, $|\\lambda_{ij}|=1$. Irreducible representations of such a families are described up to the unitary equivalence. Namely any such representation corresponds, up to the unitary equivalence, to irreducible representation of certain higher-dimensional non-commutative torus. - On q-tensor products of Cuntz algebras
Alexey Kuzmin, Vasyl Ostrovskyi, Danylo Proskurin, Moritz Weber, and Roman Yakymiv
World Scientific Pub Co Pte Ltd
We consider the [Formula: see text]-algebra [Formula: see text], which is a [Formula: see text]-twist of two Cuntz–Toeplitz algebras. For the case [Formula: see text], we give an explicit formula which untwists the [Formula: see text]-deformation showing that the isomorphism class of [Formula: see text] does not depend on [Formula: see text]. For the case [Formula: see text], we give an explicit description of all ideals in [Formula: see text]. In particular, we show that [Formula: see text] contains a unique largest ideal [Formula: see text]. We identify [Formula: see text] with the Rieffel deformation of [Formula: see text] and use a K-theoretical argument to show that the isomorphism class does not depend on [Formula: see text]. The latter result holds true in a more general setting of multiparameter deformations. - Geometric properties of SIC-POVM tensor square
Vasyl Ostrovskyi and Danylo Yakymenko
Springer Science and Business Media LLC - A CLASS OF REPRESENTATIONS OF C* -ALGEBRA GENERATED BY q<inf>ij</inf>-COMMUTING ISOMETRIES
Olha Ostrovska, Vasyl Ostrovskyi, Danylo Proskurin, and Yurii Samoilenko
National Pedagogical Dragomanov University - A Resolvent Approach to the Real Quantum Plane
Vasyl Ostrovskyi and Konrad Schmüdgen
Springer Science and Business Media LLC - On pairs of quadratically related operators
V. L. Ostrovskyi and Yu. S. Samoilenko
Springer Science and Business Media LLC - On the structure of homogenenous wick ideals in wick <inf>*</inf>- algebras with braided coefficients
VASYL OSTROVSKYI, DANIIL PROSKURIN, YURII SAVCHUK, and LYUDMILA TUROWSKA
World Scientific Pub Co Pte Lt
We study a Wick ideal structure of quadratic *-algebras allowing Wick ordering with braided operator of coefficients. A construction of nested sequence of homogeneous Wick ideals of growing degree is presented. Representations of a Wick analogue of the CCR algebra with two degrees of freedom, annihilating certain homogeneous Wick ideals are described. - Unbounded representations of q-deformation of cuntz algebra
Vasyl Ostrovskyi, Daniil Proskurin, and Lyudmila Turowska
Springer Science and Business Media LLC - On C<sup>*</sup>-algebra of a semigroup of partial isometries
Vasyl Ostrovskyi, Stanislav Popovych, and Lyudmila Turowska
Elsevier BV - On functions on graphs and representations of a certain class of *-algebras
Sergio Albeverio, Vasyl Ostrovskyi, and Yurii Samoilenko
Elsevier BV - On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs
V. L. Ostrovs’kyi and Yu. S. Samoilenko
Springer Science and Business Media LLC - Representation of an algebra associated with the Dynkin graph Ẽ <inf>7</inf>
V. L. Ostrovs’kyi
Springer Science and Business Media LLC - Representation Theory and Numerical AF-Invariants: The Representations and Centralizers of Certain States on script O sing
d
- On representations of *-algebras in mathematical physics
A.A. Mohammad and M. Can
Springer Science and Business Media LLC
1. The theory of representations ofA (∗-homomorphisms π:A 7→ L(H) of a ∗-algebraA into a ∗-algebra L(H) of all bounded operators or into a ∗-algebra of unbounded operators in a separable complex Hilbert space H) is important both in mathematics and in physical applications. The ∗-representations of A (a local object) contain information about the structure of the algebra itself as well as about the structure of its dual object. Studying a particular class of representations of A in general by unbounded operators allows to define the corresponding non-commutative manifold: a C∗-algebra A (a global object) which possesses this class of representations. A choice of a particular representation π(·) corresponds to the choice of a model with observables Ak = π(ak) (k = 1, . . . , n) obeying the relations - Representations of *-algebras and many-dimensional dynamical systems
V. L. Ostrovskii and L. B. Turovskaya
Springer Science and Business Media LLC - Representations of *-algebras and dynamical systems
Vasyl' L. Ostrovs'kyĭ and Yurii S. Samoilenko
Springer Science and Business Media LLC
Here Pk(·) are polynomials in the non-commuting variables a1, . . . , an over C such that P ∗ k (·) = Pk(·). In other words, A is a quotient of the free ∗-algebra C〈a1, . . . , an〉 generated by the self-adjoint elements a1, . . . , an with respect to the two-sided ideal generated by the relations (1). Representations ot A (∗-homomorphisms π:A → L(H) of the ∗-algebra A into a ∗algebra L(H) of bounded operators on a separable Hilbert space H or into a ∗-algebra of unbounded operators) are of interest both from mathematical point of view and for their physical applications. A choice of a representation π(·) corresponds to a choice of a model with observables Ak = π(ak) (k = 1, . . . , n), which are connected by the relations Pk(A1, . . . , An) = 0 (k = 1, . . . ,m). (2) - On representations of the Heisenberg relations for the quantum E(2) group
V. L. Ostrovs'kyi and Yu. S. Samoilenko
Springer Science and Business Media LLC - Representations of quadratic *-algebras by bounded and unbounded operators
Vasyl L. Ostrovskyĭ and YuriĭS. Samoĭlenko
Elsevier BV - On pairs of unbounded self-adjoint operators satisfying an algebraic relation
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC - Representations of real-valued forms of the graded analogue of a Lie algebra
V. L. Ostrovskii and S. D. Sil'vestrov
Springer Science and Business Media LLC - Representations of *-algebras with two generators and polynomial relations
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC - Families of unbounded self-adjoint operators connected by non-Lie relations
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC - Unbounded operators satisfying non-lie commutation relations
V.L. Ostrovskii and Yu.S. Samoilenko
Elsevier BV - An application of the projective spectral theorem to commuting families of operators
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC - Expansion in eigenfunctions of families of commuting operators and representations of commutation relations
Yu. M. Berezanskii, V. L. Ostrovskii, and Yu. S. Samoilenko
Springer Science and Business Media LLC
RECENT SCHOLAR PUBLICATIONS
- On families of twisted power partial isometries
VL Ostrovskyi, DP Proskurin, RY Yakymiv
Carpathian Mathematical Publications 14 (1), 260-265 2022 - On -tensor products of Cuntz algebras
A Kuzmin, V Ostrovskyi, D Proskurin, M Weber, R Yakymiv
International Journal of Mathematics 33 (02), 2250017 2022 - Geometric properties of SIC-POVM tensor square
V Ostrovskyi, D Yakymenko
Letters in Mathematical Physics 112 (1), 7 2022 - A class of representations of -algebra generated by -commuting isometries
O Ostrovska, V Ostrovskyi, D Proskurin, Y Samoilenko
arXiv preprint arXiv:2111.13059 2021 - On representations of q_ij-commuting isometries
V Ostrovskyi, O Ostrovska, D Proskurin, Y Samoilenko
2021 - Про зображення алгебр, породжених скінченним розкладом одиниці та набором ортогональних проекторів
EN Ashurova, VL Ostrovskyi, YS Samoilenko
Reports of the National Academy of Sciences of Ukraine, 3-9 2017 - On representations of “all but two” algebras
EN Ashurova, VL Ostrovskyi
Zbirnyk Prats Instytutu Matematyky NAN Ukrainy 12, 8-21 2015 - A resolvent approach to the real quantum plane
V Ostrovskyi, K Schmdgen
Integral Equations and Operator Theory 79, 451-476 2014 - Some remarks on Hilbert representations of posets
V Ostrovskyi, S Rabanovich
arXiv preprint arXiv:1312.2920 2013 - О парах операторов, связанных квадратичным соотношением
ВЛ Островский, ЮС Самойленко
Функциональный анализ и его приложения 47 (1), 82-87 2013 - Зображення канонічних антикомутаційних співвідношень з умовою ортогональності
ВЛ Островський, ОВ Островська, ДП Проскурін, РЯ Якимів
2013 - Representations of relations with orthogonality condition and their deformations
VL Ostrovskyi, DP Proskurin, RY Yakymiv
Methods of Functional Analysis and Topology 18 (04), 373-386 2012 - On the Structure of Homogenenous Wick Ideals in Wick*-ALGEBRAS with Braided Coefficients
V Ostrovskyi, D Proskurin, Y Savchuk, L Turowska
Reviews in Mathematical Physics 24 (04), 1250007 2012 - Конечномерный линейный анализ. I. Линейные операторы в конечномерных векторных пространствах (L)
МА Муратов, ВЛ Островский, ЮС Самойленко
Киев: Центр учеб. лит 2011 - Unbounded Representations of q-Deformation of Cuntz Algebra
V Ostrovskyi, D Proskurin, L Turowska
Letters in Mathematical Physics 85 (2), 147-162 2008 - On C∗-algebra of a semigroup of partial isometries
V Ostrovskyi, S Popovych, L Turowska
Journal of Functional Analysis 251 (1), 210-231 2007 - On quadruples of linearly connected projections and transitive systems of subspaces
Y Moskaleva, V Ostrovskyi, K Yusenko
Methods of Functional Analysis and Topology 13 (01), 43-49 2007 - On functions on graphs and representations of a certain class of∗-algebras
S Albeverio, V Ostrovskyi, Y Samoilenko
Journal of Algebra 308 (2), 567-582 2007 - On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs
VL Ostrovs’ kyi, YS Samoilenko
Ukrainian Mathematical Journal 58 (11), 1768-1785 2006 - Special characters on star graphs and representations of -algebras
V Ostrovskyi
arXiv preprint math/0509240 2005
MOST CITED SCHOLAR PUBLICATIONS
- Introduction To The Theory Of Representations of Finitely Presented *-Algebras. I. Representations by Bounded Operators
V Ostrovskyi, Y Samoilenko
CRC Press 2004
Citations: 192 - Representation theory and numerical AF-invariants: The representations and centralizers of certain states on Od
O Bratteli, PET Jrgensen, V Ostrovsʹkyĭ
American Mathematical Soc. 168 (797) 2004
Citations: 44 - On functions on graphs and representations of a certain class of∗-algebras
S Albeverio, V Ostrovskyi, Y Samoilenko
Journal of Algebra 308 (2), 567-582 2007
Citations: 39 - Unbounded operators satisfying non-Lie commutation relations
VL Ostrovskii, YS Samoilenko
Reports on mathematical physics 28 (1), 91-104 1989
Citations: 30 - On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs
VL Ostrovs’ kyi, YS Samoilenko
Ukrainian Mathematical Journal 58 (11), 1768-1785 2006
Citations: 21 - On pairs of self-adjoint operators
VL Ostrovskyı, YS Samoılenko
Seminar Sophus Lie 3 (2), 185-218 1993
Citations: 18 - Expansion in eigenfunctions of families of commuting operators and representations of commutation relations
YM Berezanskii, VL Ostrovskii, YS Samoilenko
Ukrainian Mathematical Journal 40, 90-92 1988
Citations: 15 - Representations of real-valued forms of the graded analogue of a Lie algebra
VL Ostrovskii, SD Sil'vestrov
Ukrainian Mathematical Journal 44 (11), 1395-1401 1993
Citations: 14 - On*-representations of a certain class of algebras related to a graph
V Ostrovskyi
arXiv preprint math/0506505 2005
Citations: 13 - Representations of -algebras with two generators and polynomial relations
VL Ostrovskii, YS Samoilenko
Zapiski Nauchnykh Seminarov POMI 172, 121-129 1989
Citations: 13 - On -tensor products of Cuntz algebras
A Kuzmin, V Ostrovskyi, D Proskurin, M Weber, R Yakymiv
International Journal of Mathematics 33 (02), 2250017 2022
Citations: 12 - Families of unbounded self-adjoint operators connected by non-Lie relations
VL Ostrovskii, YS Samoilenko
Functional Analysis and Its Applications 23 (2), 139-141 1989
Citations: 12 - Representations of∗-algebras and multidimensional dynamical systems
VL Ostrovskyı, LB Turovskaya
Ukr. Mat. Zhurn 47 (4), 488-497 1995
Citations: 11 - Structure theorems for a pair of unbounded selfadjoint operators satisfying quadratic relation
VL Ostrovskii, YS Samoilenko
Akad. Nauk Ukrain. SSR. Inst. Mat. Preprint, 1-25 1991
Citations: 11 - Representations of quadratic∗-algebras by bounded and unbounded operators
VL Ostrovskyĭ, YS Samoĭlenko
Reports on Mathematical Physics 35 (2-3), 283-301 1995
Citations: 9 - Representations of the real forms of a graded analogue of the Lie algebra sl (2, C)
VL Ostrovskyi, SD Silvestrov
Ukr. Mat. Zhurn 44 (11), 1518-1524 1992
Citations: 9 - Unbounded Representations of q-Deformation of Cuntz Algebra
V Ostrovskyi, D Proskurin, L Turowska
Letters in Mathematical Physics 85 (2), 147-162 2008
Citations: 8 - Special characters on star graphs and representations of -algebras
V Ostrovskyi
arXiv preprint math/0509240 2005
Citations: 8 - Samoılenko Yu
VL Ostrovskyı
S., Unbounded operators satisfying non-Lie commutation relations, Repts 1989
Citations: 8 - Geometric properties of SIC-POVM tensor square
V Ostrovskyi, D Yakymenko
Letters in Mathematical Physics 112 (1), 7 2022
Citations: 7