Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-23T08:09:18.511Z Has data issue: false hasContentIssue false
  • English
  • Français

THE DUALITY PROBLEM FOR THE CLASS OF ORDER WEAKLY COMPACT OPERATORS

Published online by Cambridge University Press:  01 January 2009

BELMESNAOUI AQZZOUZ  and
JAWAD HMICHANE
BELMESNAOUI AQZZOUZ
Affiliation:
Université Mohammed V-Souissi, Faculté des Sciences Economiques, Juridiques et Sociales, Département d'Economie, B.P. 5295, SalaEljadida, Morocco e-mail: baqzzouz@hotmail.com
JAWAD HMICHANE
Affiliation:
Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, B.P. 133, Kénitra, 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 study the duality problem for order weakly compact operators by giving sufficient and necessary conditions under which the order weak compactness of an operator implies the order weak compactness of its adjoint and conversely.

Keywords

46A4046B4046B42
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 101 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Aliprantis, C. D. and Burkinshaw, O., Locally solid Riesz spaces (Academic Press, New York, 1978).Google Scholar
2.Aliprantis, C. D. and Burkinshaw, O., On weakly compact operators on Banach lattices, Proc. Amer. Math. Soc. 83 (3), (1981) 573–578.CrossRefGoogle Scholar
3.Aliprantis, C. D. and Burkinshaw, O., Positive operators, in Pure and applied mathematics, Vol. 119 (Academic Press, Orlando, FL, 1985).Google Scholar
4.Aqzzouz, B. and Nouira, R., Sur les opérateurs précompacts positifs, C. R. Acad. Sc. Paris 337 (8) (2003) 527–530.CrossRefGoogle Scholar
5.Aqzzouz, B., Nouira, R. and Zraoula, L., The duality problem for the class of AM-compact operators on Banach lattices, Can. Math. Bull. 51 (1) (2008) 15–20.CrossRefGoogle Scholar
6.Dodds, P. G., o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214 (1975), 389–402.Google Scholar
7.Duhoux, M., o-weakly compact mappings from a Riesz space to a locally convex space, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 22 (4)(70) (1978), 371–378.Google Scholar
8.Ercan, Z., Interval-bounded operators and order weakly compact operators on Riesz spaces, Demonstr. Math. 31 (4) (1998), 805–812.Google Scholar
9.Josefson, B., Weak sequential convergence in the dual of a Banach space does not imply norm convergence, Ark. Mat. 13 (1975), 79–89.CrossRefGoogle Scholar
10.Meyer-Nieberg, P., Banach lattices (Universitext, Springer-Verlag, Berlin, 1991).CrossRefGoogle Scholar
11.Nissenzweig, A., w*-sequential convergence, Israel J. Math. 22 (3–4) (1975), 266–272.CrossRefGoogle Scholar
12.Nowak, M., Order-weakly compact operators from vector-valued function spaces to Banach spaces, Proc. Amer. Math. Soc. 135 (9) (2007), 2803–2809.CrossRefGoogle Scholar
13.Wickstead, A. W., Extremal structure of cones of operators, Quart. J. Math. Oxford 32 (2) (1981), 239–253.CrossRefGoogle Scholar
14.Wickstead, A. W., Converses for the Dodds-Fremlin and Kalton-Saab theorems, Math. Proc. Camb. Phil. Soc. 120 (1996), 175–179.CrossRefGoogle Scholar
15.Wnuk, W., A note on the positive Schur property, Glasgow Math. J. 31 (1989), 169–172.CrossRefGoogle Scholar
16.Zaanen, A. C., Riesz spaces II (North Holland Publishing Company, 1983).Google Scholar