Order bornological locally convex lattice cones

Автор: Ayaseh Davood, Ranjbari Asghar

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.19, 2017 года.

Бесплатный доступ

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.

Locally convex lattice cones, order bornological cones

Короткий адрес: https://sciup.org/14318578

IDR: 14318578   |   DOI: 10.23671/VNC.2017.3.7109

Список литературы Order bornological locally convex lattice cones

  • Aliprantis C. D., Burkinshaw O. Positive Operators. N.Y.: Acad. Press, 1985. xvi+367 p.
  • Ayaseh D., Ranjbari A. Bornological convergence in locally convex cones. Mediterr. J. Math., 2016, vol. 13(4), pp. 1921-1931.
  • Ayaseh D., Ranjbari A. Bornological locally convex cones. Le Matematiche, 2014, vol. 69(2), pp. 267-284.
  • Ayaseh D., Ranjbari A. Locally convex quotient lattice cones. Math. Nachr., 2014, vol. 287(10), pp. 1083-1092.
  • Keimel K., Roth W. Ordered Cones and Approximation. Heidelberg-Berlin-N.Y.: Springer Verlag, 1992. (Lecture Notes in Math.; vol. 1517).
  • Ranjbari A. Strict inductive limits in locally convex cones. Positivity, 2011, vol. 15(3), pp. 465-471.
  • Ranjbari A., Saiflu H. Projective and inductive limits in locally convex cones. J. Math. Anal. Appl., 2007, vol. 332, pp. 1097-1108.
  • Robertson A. P., Robertson W. Topological Vector Spaces. Cambridge: Cambridge Univ. Press, 1964. viii+158 p. (Cambridge Tracts in Math.; vol. 53).
  • Roth W. Locally convex quotient cones. J. Convex Anal., 2011, vol. 18, no. 4, pp. 903-913.
  • Roth W. locally convex lattice cones. J. Convex Anal., 2009, vol. 16, no. 1, pp. 1-8.
  • Roth W. Operator-Valued Measures and Integrals for Cone-Valued Functions. Heidelberg-Berlin-N.Y.: Springer Verlag, 2009. (Lecture Notes in Math.; vol. 1964).
Еще
Статья научная