Have a personal or library account? Click to login
A note on the relationship between three classes of operators on Riesz spaces Cover

A note on the relationship between three classes of operators on Riesz spaces

By: Liang Hong  
Open Access
|Dec 2020

References

  1. [1] C. D. Aliprantis, On order properties of order bounded transformations, Can. J. Math., XXVII/3, (1975), 666–67810.4153/CJM-1975-075-8
  2. [2] C. D. Aliprantis and O. Burkinshaw, On positive order continuous operators, Indag. Math., 86/1, (1983), 1–610.1016/1385-7258(83)90036-7
  3. [3] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Sprinter, Berlin, 1985
  4. [4] C. D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Second Edition, American Mathematical Society, Providence, Rhode Island, 200310.1090/surv/105
  5. [5] N. Bourbaki, Elements of Mathematics: Topological Vector Spaces, Springer, Berlin, 198710.1007/978-3-642-61715-7
  6. [6] N. Erkursun–Ozcan, N. A. Gezer, and O. Zabeti, Spaces of μτ -Dunford-Pettis and μτ -compact operators on locally solid vector lattices, https://arxiv.org/abs/1710.11434, (2017)
  7. [7] L. Hong, On order bounded subsets of locally solid Riesz spaces, Quaestiones Mathematicae, 39/3, (2016), 381–38910.2989/16073606.2015.1070380
  8. [8] J. Horváth, Topological Vector Spaces and Distributions, Vol. I, Addison-Wesley, Reading, Massachusetts, 1966
  9. [9] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces, Vol. I, North-Holland, Amsterdam, 1971
  10. [10] H. Nakano, Modulared Semi-ordered Linear Spaces, Maruzen Co., Tokyo, 1950
  11. [11] H. Nakano, Linear Lattices, Wayne State University Press, Detroit, MI, 1966
  12. [12] L. Narici and E. Beckenstein, Topological Vector Spaces, Second Edition,CRC Press, Boca Raton, 201110.1201/9781584888673
  13. [13] G. T. Roberts, Topologies in vector lattices, Math. Proc. Cambridge Phil. Soc., 48, (1952), 533–54610.1017/S0305004100076295
  14. [14] H. H. Schaefer, Topological Vector Spaces, Sprinter, Berlin, 1974
  15. [15] H. H. Schaefer, On order continuous linear operators, Indag. Math., 92/4, (1989), 479–48310.1016/1385-7258(89)90011-5
  16. [16] H. H. Schaefer, Topological algebras of locally solid vector subspaces of order bounded operators, Positivity, 21, (2017), 1253–125910.1007/s11117-016-0464-7
  17. [17] A. C. Zaanen, Introduction to Operator Theory in Riesz Spaces, Sprinter, Berlin, 199710.1007/978-3-642-60637-3
DOI: https://doi.org/10.2478/awutm-2019-0016 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 77 - 85
Published on: Dec 21, 2020
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2020 Liang Hong, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.