On families of twisted power partial isometries V.L. Ostrovskyi, D.P. Proskurin, R.Ya. Yakymiv Carpathian Mathematical Publications, 2022 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, Roman Yakymiv International Journal of Mathematics, 2022 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.
On the structure of homogenenous wick ideals in wick *- algebras with braided coefficients VASYL OSTROVSKYI, DANIIL PROSKURIN, YURII SAVCHUK, LYUDMILA TUROWSKA Reviews in Mathematical Physics, 2012 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.
Representation Theory and Numerical AF-Invariants: The Representations and Centralizers of Certain States on script O sing d Memoirs of the American Mathematical Society, 2004
On quantum symmetries of graphs O Ostrovska, V Ostrovskyi, L Turowska arXiv preprint arXiv:2603.09401 , 2026 2026
On families of twisted power partial isometries VL Ostrovskyi, DP Proskurin, RY Yakymiv Carpathian Mathematical Publications 14 (1), 260-265 , 2022 2022 Citations: 1
On -tensor products of Cuntz algebras A Kuzmin, V Ostrovskyi, D Proskurin, M Weber, R Yakymiv International Journal of Mathematics 33 (02), 2250017 , 2022 2022 Citations: 13
Geometric properties of SIC-POVM tensor square V Ostrovskyi, D Yakymenko Letters in Mathematical Physics 112 (1), 7 , 2022 2022 Citations: 7
A class of representations of -algebra generated by -commuting isometries O Ostrovska, V Ostrovskyi, D Proskurin, Y Samoilenko arXiv preprint arXiv:2111.13059 , 2021 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 ЕН Ашурова, ВЛ Островський, ЮС Самойленко Reports of the National Academy of Sciences of Ukraine, 3-9 , 2017 2017
On representations of “all but two” algebras EN Ashurova, VL Ostrovskyi Zbirnyk Prats Instytutu Matematyky NAN Ukrainy 12, 8-21 , 2015 2015 Citations: 5
A resolvent approach to the real quantum plane V Ostrovskyi, K Schmüdgen Integral Equations and Operator Theory 79 (4), 451-476 , 2014 2014 Citations: 1
Some remarks on Hilbert representations of posets V Ostrovskyi, S Rabanovich arXiv preprint arXiv:1312.2920 , 2013 2013 Citations: 1
О парах операторов, связанных квадратичным соотношением ВЛ Островский, ЮС Самойленко Функциональный анализ и его приложения 47 (1), 82-87 , 2013 2013 Citations: 6
Representations of relations with orthogonality condition and their deformations RY Yakymiv, DP Proskurin, VL Ostrovskyi Methods of Functional Analysis and Topology 18 (4), 373-386 , 2012 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 2012 Citations: 1
Конечномерный линейный анализ. I. Линейные операторы в конечномерных векторных пространствах (L) МА Муратов, ВЛ Островский, ЮС Самойленко Киев: Центр учеб. лит , 2011 2011 Citations: 5
Unbounded Representations of q -Deformation of Cuntz Algebra V Ostrovskyi, D Proskurin, L Turowska Letters in Mathematical Physics 85 (2), 147-162 , 2008 2008 Citations: 7
On C∗-algebra of a semigroup of partial isometries V Ostrovskyi, S Popovych, L Turowska Journal of Functional Analysis 251 (1), 210-231 , 2007 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 2007 Citations: 1
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 2007 Citations: 39
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 2006 Citations: 26
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 2004 Citations: 192
Representation theory and numerical AF-invariants: The representations and centralizers of certain states on Od O Bratteli, PET Jørgensen, V Ostrovsʹkyĭ American Mathematical Soc. 168 (797) , 2004 2004 Citations: 47
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 2007 Citations: 39
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 2006 Citations: 26
On pairs of self-adjoint operators VL Ostrovskyı, YS Samoılenko Seminar Sophus Lie 3 (2), 185-218 , 1993 1993 Citations: 17
Eigenfunction expansion of families of commuting operators and representations of commutation relations YM Berezansky, VL Ostrovsky, YS Samoilenko Ukr. Mat. Zh. 40 (1), 108-109 , 1988 1988 Citations: 17
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 1993 Citations: 14
On -tensor products of Cuntz algebras A Kuzmin, V Ostrovskyi, D Proskurin, M Weber, R Yakymiv International Journal of Mathematics 33 (02), 2250017 , 2022 2022 Citations: 13
On*-representations of a certain class of algebras related to a graph V Ostrovskyi arXiv preprint math/0506505 , 2005 2005 Citations: 12
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 1992 Citations: 12
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 1991 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 1989 Citations: 12
Representations of -algebras with two generators and polynomial relations VL Ostrovskii, YS Samoilenko Zapiski Nauchnykh Seminarov POMI 172, 121-129 , 1989 1989 Citations: 12
