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Order-continuous component of a majorized operator

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Literature Cited

  1. N. Dunford and J. T. Schwartz, Linear Operators, Part 1, General Theory, Interscience, New York (1958).

    Google Scholar 

  2. A. D. Aleksandrov, [A. D. Alexandroff], “Additive set functions in abstract spaces”, Mat. Sb.,8 (50), No. 2, 307–348 (1940);9 (51), No. 3, 563–628 (1941);13 (55), Nos. 2–3, 169–238 (1943).

    Google Scholar 

  3. M. A. Woodbury, “A decomposition theorem for finitely additive set functions” Bull. Am. Math. Soc.,56, No. 2, 171–172 (1950).

    Google Scholar 

  4. L. J. Heider, “A representation theory for measures on Boolean algebras”, Mich. Math., J.,5, No. 2, 213–221 (1958).

    Google Scholar 

  5. J. L. Kelley, “Measures on Boolean algebras”, Pac. J. Math.,9, No. 4, 1165–1177 (1959).

    Google Scholar 

  6. A. N. Dolgushev, “Remarks on finitely additive measures”, Sib. Mat. Zh.,22, No. 2, 105–120 (1981).

    Google Scholar 

  7. E. Hewitt and K. Yosida, “Finitely additive measures”, Trans. Am. Math. Soc.,72, No. 1, 46–66 (1952).

    Google Scholar 

  8. T. Traynor, “A general Hewitt-Yosida decomposition”, Can. J. Math.,24, No. 2, 1164–1169 (1972).

    Google Scholar 

  9. T. Traynor, “The Lebesgue decomposition for group valued set functions”, Trans. Am. Math. Soc.,220, 307–319 (1976).

    Google Scholar 

  10. J. J. Uhl Jr., “Extensions and decompositions of vector measures”, J. London Math. Soc.,3, No. 4, 672–676 (1971).

    Google Scholar 

  11. J. A. Crenshaw and R. B. Kirk, “Group valued, α-additive set functions”, Stud. Math.,65, No. 2, 89–101 (1979).

    Google Scholar 

  12. L. Drewnowski, “Decomposition of set functions”, Stud. Math.,48, No. 1, 23–48 (1973).

    Google Scholar 

  13. P. McGill, “Measure extensions and decompositions: A topological approach”, Proc. R. Irish. Acad. A.,81, No. 2, 157–169 (1981).

    Google Scholar 

  14. L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis and Partially Ordered Spaces [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  15. B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces [in Russian], Gostekhizdat, Moscow (1961).

    Google Scholar 

  16. W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces. I, North-Holland, Amsterdam (1971).

    Google Scholar 

  17. H. Gordon and E. R. Lorch, “The projection of a linear functional on the manifold of integrals”, Can. J. Math.,9, No. 4, 465–474 (1957).

    Google Scholar 

  18. W. A. J. Luxemburg and A. C. Zaanen, “Notes on Banach function space. VI”, Indag. Math.,25, No. 5, 655–668 (1963).

    Google Scholar 

  19. W. A. J. Luxemburg, “Notes on Banach function spaces. XV”, Indag. Math.,27, No. 3, 415–446 (1965).

    Google Scholar 

  20. W. A. J. Luxemburg, “Notes on Banach function spaces. XVI”, Indag. Math.,27, No. 4, 646–667 (1965).

    Google Scholar 

  21. C. D. Aliprantis, “On order projections of order bounded transformations”, Can. J. Math.,27, No. 3, 666–678 (1975).

    Google Scholar 

  22. A. R. Schep, “Order continuous components of operators and measures”, Indag. Math.,40, No. 1, 110–117 (1978).

    Google Scholar 

  23. P. van Eldik, “The integral component of an order bounded transformation”, Quaestiones Math.,1, No. 2, 135–144 (1976).

    Google Scholar 

  24. C. D. Aliprantis and O. Burkinshaw, “On positive order continuous operators”, Indag. Math.,45, No. 1, 1–6 (1983).

    Google Scholar 

  25. A. G. Kusraev, Vector Duality and Its Applications [in Russian], Nauka, Novosibirsk (1985).

    Google Scholar 

  26. A. G. Kusraev and V. Z. Strizhevskii, “Lattice-normed spaces and majorized operators”, in: Investigations in Geometry and Mathematical Analysis [in Russian], Vol. 7, Trudy Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Nauka, Novosibirsk (1987), pp. 132–157.

    Google Scholar 

  27. A. G. Pinsker, “On the representation of a K-space in the form of a ring of self-adjoint operators”, Dokl. Akad. Nauk SSSR,106, No. 2, 195–198 (1956)

    Google Scholar 

  28. G. Ya. Lozanovskii, “On the almost integral operators in KB-spaces”, Vestn. Leningr. Gos. Univ., Ser. Mat., Mekh., Astron., No. 7, 35–44 (1966).

    Google Scholar 

  29. A. C. Zaanen, Riesz Spaces. II, North-Holland, Amsterdam (1983).

    Google Scholar 

  30. B. de Pagter, “The components of a positive operator”, Indag. Math.,45, No. 2, 229–241 (1983).

    Google Scholar 

  31. C. D. Aliprantis and O. Burkinshaw, “The components of a positive operator”, Math. Z.,184, No. 2, 245–257 (1983).

    Google Scholar 

  32. C. D. Aliprantis and O. Burkinshaw, “Projecting onto the band of kernel operators” Houston J. Math.,11, No. 1, 7–14 (1985).

    Google Scholar 

  33. K. Matthes, “Über die Ausdehnung positive linear Abbildungen”, Math. Nachr.,23 223–257 (1961).

    Google Scholar 

  34. J. D. M. Wright, “An extension theorem” J. London Math. Soc.,7, 531–539 (1973).

    Google Scholar 

  35. D. H. Fremlin, “A direct proof of the Matthes-Wright integral extension theorem”, J. London Math. Soc.,11, No. 3, 276–284 (1985).

    Google Scholar 

  36. J. D. M. Wright, “The measure extension theorem for vector lattices”, Ann. Inst. Fourier (Grenoble),21, No. 4 65–85 (1971).

    Google Scholar 

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Authors
  1. A. G. Kusraev
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  2. S. A. Malyugin
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Additional information

Dedicated to A. D. Aleksandrov on his 70th birthday.

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 4, pp. 127–139, July–August, 1987.

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Kusraev, A.G., Malyugin, S.A. Order-continuous component of a majorized operator. Sib Math J 28, 617–627 (1987). https://doi.org/10.1007/BF00973851

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