Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-07-06T16:00:19.088Z Has data issue: false hasContentIssue false
  • English
  • Français

The Duality Problem for the Class of AM-Compact Operators on Banach Lattices

Published online by Cambridge University Press:  20 November 2018

Belmesnaoui Aqzzouz ,
Redouane Nouira  and
Larbi Zraoula
Belmesnaoui Aqzzouz
Affiliation:
Université Mohammed V-Souissi, Faculté des Sciences Economiques, Juridiques et Sociales, Départment d’Economie, B.P. 5295, Sala Eljadida, Morocco e-mail: baqzzouz@hotmail.com
Redouane Nouira
Affiliation:
Université Ibn Tofail, Département de Mathématiques, B.P. 133, Kenitra, Morocco
Larbi Zraoula
Affiliation:
Université Ibn Tofail, Département de Mathématiques, B.P. 133, Kenitra, Morocco
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove the converse of a theorem of Zaanen about the duality problem of positive $\text{AM}$-compact operators.

Keywords

46A4046B4046B42
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 1 , 01 March 2008 , pp. 15 - 20
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Aliprantis, C. D. and Burkinshaw, O., Locally Solid Riesz Spaces. Pure and Applied Mathematics 76, Academic Press, New York, 1978.Google Scholar
[2] Aliprantis, C. D. and Burkinshaw, O., Positive compact operators on Banach lattices. Math. Z. 174(1980), no. 3, 289–298.Google Scholar
[3] Aqzzouz, B. and Nouira, R., Sur les opérateurs précompacts positifs. C. R. Math. Acad. Sci. Paris 337(2003), no. 8, 527–530.Google Scholar
[4] Fremlin, D. H., Riesz spaces with the order continuity property. I. Math. Proc. Cambridge Philos. Soc. 81(1977), no. 1, 31–42.Google Scholar
[5] Wickstead, A. W., Converses for the Dodds-Fremlin and Kalton-Saab theorems. Math. Proc. Cambridge. Philos. Soc. 120(1996), 175–179.Google Scholar
[6] Zaanen, A. C., Riesz Spaces. II. North-Holland Mathematical Library 30, North-Holland, Amsterdam, 1983. (Aqzzouz)Google Scholar