1683-3414 1814-0807 Владикавказский математический журнал Vladikavkaz Mathematical Journal Южный математический институт - филиал Федерального государственного бюджетного учреждения науки Федерального научного центра «Владикавказский научный центр Российской академии наук» (ЮМИ ВНЦ РАН) К автоматической ограниченности некоторых операторов между упорядоченными и топологическими векторными пространствами 10.46698/i3984-2243-2985-z 18578 03 2026 28 1 62 67 https://vmj.ru/eng/archive/detail.php?ELEMENT_ID=&SECTION_ID=658 Емельянов Э. Ю. emelanov@math.nsc.ru Институт математики им. С. Л. Соболева, РОССИЯ, 630090, Новосибирск, пр. ак. Коптюга, 4 , упорядоченное векторное пространство топологическое векторное пространство упорядоченное банахово пространство порядково-топологически ограниченный оператор порядково-топологически непрерывный оператор 1 Alpay, S., Emelyanov, E. and Gorokhova, S. \(o\tau\)-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces, Results in Mathematics, 2022, vol. 77, article no. 117. DOI: 10.1007/s00025-022-01650-3. 2 Emelyanov, E. Collective Order Convergence and Collectively Qualified Sets of Operators, Siberian Electronic Mathematical Reports, arxiv.org/pdf/2408.03671 (to appear). 3 Emelyanov, E. On Automatic Boundedness of Some Operators in Ordered Banach Spaces, arxiv.org/pdf/2503.18834. 4 Emelyanov, E., Erkursun-Ozcan, N. and Gorokhova, S. Collective Order Boundedness of Sets of Operators Between Ordered Vector Spaces, Results in Mathematics, 2025, vol. 80, article no. 70. DOI: 10.1007/s00025-025-02386-6. 5 Jalili, S. A., Azar, K. Y. and Moghimi, M. B. F. Order-to-Topology Continuous Operators, Positivity, 2021, vol. 25, pp. 1313-1322. DOI: 10.1007/s11117-021-00817-6. 6 Keles, C. S., Turan, B. and Altin, B. Order Structure of Order-to-Topological Continuous Operator, Turkish Journal of Mathematics, 2025, vol. 49(2), pp. 173-184. DOI: 10.55730/1300-0098.3581. 7 Zhang, F., Shen, H. and Chen, Z. Property \((h)\) of Banach Lattice and Order-to-Norm Continuous Operators, Mathematics, 2023, vol. 11, 2747. DOI: 10.3390/math11122747. 8 Alpay, S., Emelyanov, E. and Gorokhova, S. On Collectively Almost (Limitedly, Order) \(L\)-Weakly Compact Sets of Operators, arxiv.org/pdf/2407.11885. 9 Emelyanov, E. On Collectively \(\sigma\)-Levi Sets of Operators, Vladikavkaz Mathematical Journal, 2025, vol. 27, no. 1, pp. 36-43. DOI: 10.46698/y6929-3405-2251-o. 10 Emelyanov, E. On Collectively \(L\)-Weakly Compact Sets of Operators, Analysis Mathematica, 2025, vol. 51(2), pp. 447-455. DOI: 10.1007/s10476-025-00088-3. 11 Aliprantis, C. D. and Burkinshaw, O. Locally Solid Riesz Spaces with Applications to Economics, 2nd edition, Providence, American Mathematical Society, 2003. 12 Aliprantis, C. D. and Tourky, R. Cones and Duality, Providence, American Mathematical Society, 2007. 13 Abramovich, Y. and Sirotkin, G. On Order Convergence of Nets, Positivity, 2005, vol. 9, pp. 287-292. DOI: 10.1007/s11117-004-7543-x.