Abstract: In this paper, we introduce the concepts of $us$-lattice cones and order bornological locally convex lattice cones. In the special case of locally convex solid Riesz spaces, these concepts reduce to the known concepts of seminormed Riesz spaces and order bornological Riesz spaces, respectively. We define solid sets in locally convex cones and present some characterizations for order bornological locally convex lattice cones.
Keywords: locally convex lattice cones, order bornological cones
For citation: Ayaseh D., Ranjbari A. Order Bornological Locally Convex Lattice Cones // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 21-30. DOI 10.23671/VNC.2017.3.7109
1. Aliprantis C. D., Burkinshaw O. Positive Operators. N.Y.: Acad.
Press, 1985. xvi+367 p.
2. Ayaseh D., Ranjbari A. Bornological convergence in locally convex
cones. Mediterr. J. Math., 2016, vol. 13(4), pp. 1921-1931.
3.Ayaseh D., Ranjbari A. Bornological locally convex cones. Le
Matematiche, 2014, vol. 69(2), pp. 267-284.
4. Ayaseh D., Ranjbari A. Locally convex quotient lattice cones.
Math. Nachr., 2014, vol. 287(10), pp. 1083-1092.
5. Keimel K., Roth W. Ordered Cones and Approximation.
Heidelberg-Berlin-N.Y.: Springer Verlag, 1992. (Lecture Notes in
Math.; vol. 1517).
6. Ranjbari A. Strict inductive limits in locally convex cones.
Positivity, 2011, vol. 15(3), pp. 465-471.
7. Ranjbari A., Saiflu H. Projective and inductive limits in
locally convex cones. J. Math. Anal. Appl., 2007, vol. 332, pp.
1097-1108.
8. Robertson A. P., Robertson W. Topological Vector Spaces.
Cambridge: Cambridge Univ. Press, 1964. viii+158 p. (Cambridge Tracts
in Math.; vol. 53).
9. Roth W. Locally convex quotient cones. J. Convex Anal., 2011,
vol. 18, no. 4, pp. 903-913.
10. Roth W. locally convex lattice cones. J. Convex Anal., 2009,
vol. 16, no. 1, pp. 1-8.
11. Roth W. Operator-Valued Measures and Integrals for Cone-Valued
Functions. Heidelberg-Berlin-N.Y.: Springer Verlag, 2009. (Lecture
Notes in Math.; vol. 1964).
