Abstract
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.
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Abramovich Y.A. and Aliprantis, C.D.: An Invitation to Operator Theory, American Mathematical Society, Providence, 2002.
C.D. Aliprantis O. Burkinshaw (1985) Positive Operators Academic Press New York & London
R.F. Anderson J.C. Mathews (1967) ArticleTitleA Comparison of Two Modes of Order Convergence Proc. Amer. Math. Soc. 18 100–104
Birkhoff, G.: Lattice Theory, Vol. 25, AMS Coloq. Publ. 1940.
J.L. Kelley (1955) General Topology Van Nostrand New York
G.Ya. Lozanovskii (1965) ArticleTitleTwo Remarks Concerning Operators in Partially Ordered Spaces Vestnik Leningrad Univ. Mat. Meh. Astronom. 19 159–160
W.A.J. Luxemburg A.C. Zaanen (1971) Riesz Spaces I North–Holland Amsterdam
P. Meyer-Nieberg (1991) Banach Lattices Springer-Verlag Berlin
van Rooij, A.: Personal communications.
H.H. Schaefer (1971) Topological Vector Spaces Springer-Verlag New York
H.H. Schaefer (1974) Banach Lattices and Positive Operators Springer-Verlag New York
E.S. Wolk (1961) ArticleTitleOn Order-convergence Proc. Amer. Math. Soc. 12 379–384
A.C. Zaanen (1983) Riesz Spaces. II North-Holland Publishing Co. Amsterdam-New York
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Yuri Abramovich - Lived 1945 to 2003
Yuri Abramovich- Deceased
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Abramovich, Y., Sirotkin, G. On Order Convergence of Nets. Positivity 9, 287–292 (2005). https://doi.org/10.1007/s11117-004-7543-x
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DOI: https://doi.org/10.1007/s11117-004-7543-x