ON ORDER CONTINUOUS BANACH C(K)-MODULES
Omer Gok
Yildiz Technical University
Faculty of Arts and Sciences
Mathematics Department, Davutpasa
Istanbul - 34210, TURKEY

Abstract

Let $X$ be a Banach space and let $X'$ be the norm dual of $X$. $C(K)$ denotes the Banach space of all continuous real or complex valued functions on a compact Hausdorff space $K$ with the supremum norm. Suppose that $X$ is a Banach $C(K)$-module. In this paper, we characterize the order continuity of Banach $C(K)$-module if dual Banach space $X'$ does not contain the space $\ell^{\infty}$ of all bounded sequences by using Arens multiplication.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 2
Year: 2022

DOI: 10.12732/ijam.v35i2.7

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] Yu.A. Abramovich, E.L. Arenson, A.K. Kitover, Banach C(K)-Modules and Operators Preserving Disjointness, Pitman Research Notes in Math. Ser., 277, Longman Scientific and Technical (1992).
  2. [2] R. Arens, The adjoint of bilinear operations, Proc. Amer. Math. Soc., 2 (1951), 839-848.
  3. [3] O. Gok, b-bimorphisms, International Journal of Applied Mathematics, 32, No 1 (2019), 45-50; doi: 10.12732/ijam.v32i1.4.
  4. [4] D. Hadwin, M. Orhon, A noncommutative theory of Bade functionals, Glasgow Math. J., 33 (1991), 75-81.
  5. [5] D. Hadwin, M. Orhon, Reflexivity and approximate reflexivity for Boolean algebras of projections, J. Funct. Anal., 87 (1989), 348-353.
  6. [6] A. Kitover, M. Orhon, Reflexivity of Banach C(K)-modules via reflexivity of Banach lattices, Positivity, 18, No 3 (2014), 475-488.
  7. [7] A. Kitover, M. Orhon, Dedekind complete and order continuous Banach C(K)-modules, In: Positivity and Noncommutative Analysis, Trends Math. Birkhauser-Springer (2019), 281-294.
  8. [8] P. Meyer-Nieberg, Banach Lattices, Springer, Berlin (1991).
  9. [9] G.Ya. Lozanovskii, On isomorphic Banach structure, Siberian Math. J., 10, No 1 (1969), 64-68.
  10. [10] H.H. Schaefer, Banach Lattices and Positive Operators, Springer, Berlin (1974).
  11. [11] W. Wnuk, Banach Lattices with Order Continuous Norm, Polish Scientific Publishers PWN, Warszawa (1999).