On Kakutani--Krein and Maeda--Ogasawara spaces

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Let E be an Archimedean Riesz space. It is shown that the Kakutani--Krein space of the center of the Dedekind completion of E and the Maeda--Ogasawara space of E are homeomorphic. By applying this, we can reprove a Banach Stone type theorem for C\infty(S) spaces, where S is a Stonean space.

Anahtar Kelimeler:

Riesz space, universal completion, Kakutani--Krein space, Maeda--Ogasawara space

On Kakutani--Krein and Maeda--Ogasawara spaces

Keywords:

Riesz space, universal completion, Kakutani--Krein space, Maeda--Ogasawara space,

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[1] Aliprantis, C.D., Burkinshaw, O.: Positive Operators. New York. Academic Press 1985.
[2] Aliprantis, C.D., Burkinshaw, O.: Locally Solid Riesz Spaces with Applications to Economics. Mathematical Surveys and Monographs, 105. Providence. American Mathematical Society 2003.
[3] Buskes, G.A., Van Rooij, A.C.M.: Whales and the universal completion. Proc. Amer. Math. Soc. 124, 423–427 (1996).
[4] de Jonge, E., van Rooij, A.C.M.: Introduction to Riesz Spaces. Mathematical Centre Tracts, No. 78. Amsterdam. Mathematisch Centrums 1977.
[5] Emel’yanov, E.Y.: Infinitesimal analysis and vector lattices. Siberian Adv. Math. 6, 19–70 (1996).
[6] Fl¨osser, H.O., Gierz, G., Keimel, K.: Structure spaces and the center of vector lattices. Q. J. Math. Oxford Ser. 29, 415–426 (1978).
[7] Luxemburg W.A., Zaanen, A.C.: Riesz Spaces, Volume 1. Amsterdam. North-Holland Publishing Co. 1971
[8] Maeda, F., Ogasawara, T.: Representation of vector lattices (in Japanese). J. Sci. Hiroshima Univ. Ser. A. 12, 17–35 (1942).
[9] Meyer-Nieberg, P.: Banach Lattices. Berlin. Springer Verlag 1991. [10] Vulikh, B.Z.: Introduction to the Theory of Partially Ordered Spaces. New York. Gordon and Breach 1967.
[11] Zaanen, A.C. : Introduction to Operator Theory in Riesz Spaces. Berlin. Springer-Verlag 1997.
[12] Zaanen, A.C. : Another construction of the universal completion, Indag. Math. 45, 435–441 (1983).