Automatic Boundedness of Some Operators Between Ordered and Topological Vector Spaces

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.46698/i3984-2243-2985-z Automatic Boundedness of Some Operators Between Ordered and Topological Vector Spaces Emelyanov, E. Y. Vladikavkaz Mathematical Journal 2026. Vol. 28. Issue 1. Abstract: Order-to-topology continuous operators and order-to-norm bounded operators have been recently studied by many authors mostly in the framework of Banach lattices. In the present note, we extend some of results obtained by these authors to the setting of operators from an ordered Banach space to a topological vector space. We present several conditions providing topological boundedness of such operators, and investigate uniform boundedness principle for collectively qualified families of operators, and establish uniform boundedness of power order-to-norm bounded operator semigroups on an ordered Banach space with a closed generating cone. We prove that every collectively order-to-topology bounded set of operators from an ordered Banach space to a topological vector space is collective ru-to-topology continuous and provide conditions under which such sets are uniformly bounded. Keywords: ordered vector space, topological vector space, ordered Banach space, order-to-topology bounded operator, order-to-topology continuous operator. Language: English Download the full text Download JATS XML For citation: Emelyanov, E. Yu. Automatic Boundedness of Some Operators Between Ordered and Topological Vector Spaces, Vladikavkaz Math. J., 2026, vol. 28, no. 1, pp. 62-67. DOI 10.46698/i3984-2243-2985-z + References 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. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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