On order convergence of nets

被引:54
作者
Abramovich, Y [1 ]
Sirotkin, G [1 ]
机构
[1] No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
关键词
Fourier Analysis; Operator Theory; Potential Theory; Continuous Operator; Order Convergence;
D O I
10.1007/s11117-004-7543-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we show that any order continuous operator between two Riesz spaces is automatically order bounded. We also investigate different types of order convergence.
引用
收藏
页码:287 / 292
页数:6
相关论文
共 13 条
  • [1] Abramovich Y. A., 2002, AMS
  • [2] Aliprantis C. D., 1985, POSITIVE OPERATORS
  • [3] BIRKHOFF G, 1940, AMS COLOQ PUBL, V25
  • [4] Kelley John L., 1975, GEN TOPOLOGY
  • [5] Lozanovsky G. Ya., 1965, VESTNIK LENINGRAD U, V19, P159
  • [6] Luxemburg W. A. J., 1971, Riesz spaces, VI
  • [7] A COMPARISON OF 2 MODES OF ORDER CONVERGENCE
    MATHEWS, JC
    ANDERSON, RF
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 18 (01) : 100 - &
  • [8] Meyer-Nieb erg P, 1991, Banach Lattices
  • [9] Schaefer H. H., 1974, BANACH LATTICES POSI
  • [10] SCHAEFER HH, 1971, TOPOLOGICAL VECTOR