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Order-continuous extension of a positive operator. (English. Russian original) Zbl 0770.47008
Sib. Math. J. 29, No. 5, 707-716 (1988); translation from Sib. Mat. Zh. 29, No. 5(171), 24-35 (1988).
This is an extended version of an earlier paper by the same authors [Dokl. Akad. Nauk SSSR 298, No. 3, 521-524 (1988; Zbl 0696.47035)]. The previously announced theorems are now presented with proofs and related results are also established.

MSC:
47B65 Positive linear operators and order-bounded operators
46A40 Ordered topological linear spaces, vector lattices
28B15 Set functions, measures and integrals with values in ordered spaces
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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[1] L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977). · Zbl 0127.06102
[2] L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis in Semiordered Spaces [in Russian], Gostekhizdat, Moscow-Leningrad (1950). · Zbl 0037.07201
[3] B. Z. Vulikh, Introduction to the Theory of Semiordered Spaces [in Russian], Fizmatgiz, Moscow (1961). · Zbl 0101.08501
[4] G. P. Akilov and S. S. Kutateladze, Ordered Vector Spaces [in Russian], Nauka, Novosibirsk (1978). · Zbl 0395.46010
[5] A. G. Kusraev, Vector Duality and Its Applications [in Russian], Nauka, Novosibirsk (1985). · Zbl 0616.49010
[6] W. A. J. Luxemburg and A. R. Schep, ?A Radon-N-Nikodym type theorem for positive operators and a dual,? Indagat. Math.,40, No. 3, 357-375 (1978). · Zbl 0389.47018
[7] S. S. Kutateladze, ?Convex analysis in modules,? Sib. Mat. Zh.,22, No. 4, 118-128 (1981).
[8] A. G. Kusraev and V. Z. Strizhevskii, ?Lattice normed spaces and majorizing operators,? in: Studies in Geometry and Analysis [in Russian], Nauka, Novosibirsk (1986), pp. 56-102.
[9] R. De Pagter, ?The components of a positive operator,? Indagat. Math.,45, No. 2, 229-241 (1983). · Zbl 0521.47018
[10] C. D. Aliprantis and O. Burkinschaw, ?The components of a positive operator,? Math. Z.,184, No. 2, 245-257 (1983). · Zbl 0515.47014 · doi:10.1007/BF01252860
[11] G. P. Akilov and V. N. Dyatlov, Elements of Functional Analysis [in Russian], Novosibirsk State Univ. (1979). · Zbl 0489.06012
[12] D. H. Fremlin, ?Tensor products of Archimedean vector lattices,? Am. J. Math.,94, 777-798 (1972). · Zbl 0252.46094 · doi:10.2307/2373758
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