zbMATH — the first resource for mathematics

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.

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
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.