SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 1

On Kakutani--Krein and Maeda--Ogasawara spaces

Zafer ERCAN
Neşet Özkan TAN
Pages
136–138
Publication Date
2014-05-16
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

By applying this, we can reprove a Banach Stone type theorem for C\infty(S) spaces, where S is a Stonean space.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let E be an Archimedean Riesz space.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:By applying this, we can reprove a Banach Stone type theorem for C\infty(S) spaces, where S is a Stonean space.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riesz space · universal completion · Kakutani--Krein space

Abstract

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.

Özet

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.

🔖

Cite This Article

ERCAN, Z., TAN, N. Ö. (2014). On Kakutani--Krein and Maeda--Ogasawara spaces. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 1, 136–138. https://ajindex.com/articles/723321

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  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
  4. 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)
  8. Meyer-Nieberg, P.: Banach Lattices. Berlin. Springer Verlag 1991
  9. Vulikh, B.Z.: Introduction to the Theory of Partially Ordered Spaces. New York. Gordon and Breach 1967
  10. Zaanen, A.C.: Introduction to Operator Theory in Riesz Spaces. Berlin. Springer-Verlag 1997
  11. Zaanen, A.C.: Another construction of the universal completion, Indag. Math. 45, 435–441 (1983).