Bounded Orthomorphisms Between Locally Solid Vector Lattices

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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/c1197-8093-8231-u Bounded Orthomorphisms Between Locally Solid Vector Lattices Sabbagh, R. , Zabeti, O. Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 4. Abstract: The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equivalence between orthomorphisms and the underlying vector lattice for the case of all bounded orthomomorphisms. Furthermore, we investigate topological and ordered structures for these classes of orthomorphisms, as well. In particular, we show that each class of bounded orthomorphisms possesses the Levi or the \(AM\)-properties if and only if so is the underlying locally solid vector lattice. Moreover, we establish a similar result for the Lebesgue property, as well. Keywords: orthomorphism, bounded orthomorphism, \(f\)-algebra, locally solid vector lattice Language: English Download the full text For citation: Sabbagh, R. and Zabeti, O. Bounded Orthomorphisms Between Locally Solid Vector Lattices, Vladikavkaz Math. J., 2021, vol. 23, no. 4, pp. 89-95. DOI 10.46698/c1197-8093-8231-u + References 1. Aliprantis, C. D. and Burkinshaw, O. Positive Operators, Springer, 2006. 2. Erkursun-Ozcan, N. Anil Gezer, N. and Zabeti, O. Spaces of \(u\tau\)-Dunford-Pettis and \(u\tau\)-Compact Operators on Locally Solid Vector Lattices, Matematicki Vesnik, 2019, vol. 71, no. 4, pp. 351-358. 3. Zabeti, O. AM-Spaces from a Locally Solid Vector Lattice Point of View with Applications, Bulletin. Iran. Math. Society, 2021, vol. 47, pp. 1559-1569. DOI: 10.1007/s41980-020-00458-7. 4. Aliprantis, C. D. and Burkinshaw, O. Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs, vol. 105, Providence, American Mathematical Society, 2003. 5. Zabeti, O. The Banach-Saks Property from a Locally Solid Vector Lattice Point of View, Positivity, 2021, vol. 25, pp. 1579-1583. DOI: 10.1007/s11117-021-00830-9. 6. Johnson, D. G. A Structure Theory for a Class Of Lattice-Ordered Rings, Acta Mathematica, 1960, vol. 104, no. 3-4, pp. 163-215. 7. Mirzavaziri, M. and Zabeti, O. Topological Rings of Bounded and Compact Group Homomorphisms on a Topological Ring, J. Adv. Res. Pure Math, 2011, vol. 3, no. 2, pp. 100-106. 8. Zaanen, A. C. Examples of Orthomorphisms, J. Approx. Theory, 1975, vol. 13, pp. 192-–204. 9. Hejazian, S. Mirzavaziri, M. and Zabeti, O. Bounded Operators on Topological Vector Spaces and their Spectral Radii, Filomat, 2012, vol. 26, no. 6, pp. 1283-1290. 10. Troitsky, V. G. Spectral Radii of Bounded Operators on Topological Vector Spaces, Panamer. Math. J., 2001, vol. 11, no. 3, pp. 1-35. 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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