The almost Dunford-Pettis property of semi-compact operators

• Autorzy: Aqzzouz B. , Elbour A.
• Języki publikacji: EN

Abstrakty

EN

We establish necessary and sufficient conditions for which each positive semi-compact operator (resp. the second power of a positive semi-compact operator) is almost Dunford-Pettis (resp. Dunford-Pettis).

Słowa kluczowe

EN

semi-compact operator; Dunford-Pettis operator; order continuous norm; discrete Banach lattice

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 1
• Strony: 129--142
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Aqzzouz B.

autor

Elbour A.

• Universite Mohammed V-Souissi Faculté Des Sciences Economiques, Juridiques Et Sociales Département D'economie B.P. 5295 Salaaljadida, Morocco,

Bibliografia

• [1] C. D. Aliprantis, O. Burkinshaw, Locally solid Riesz spaces, Academic Press, 1978.
• [2] C. D. Aliprantis, O. Burkinshaw, M. Duhoux, Compactness properties of abstract kernel operators, Pacific J. Math. 100(1) (1982), 1–22.
• [3] C. D. Aliprantis, O. Burkinshaw, Positive Operators, Reprint of the 1985 original, Springer, Dordrecht, 2006.
• [4] B. Aqzzouz, R. Nouira, L. Zraoula, Semi-compactness of positive Dunford–Pettis operators on Banach lattices, Proc. Amer. Math. Soc. 136 (2008), 1997–2006.
• [5] B. Aqzzouz, A. Elbour, Semi-compactness of almost Dunford–Pettis operators on Banach lattices, Demonstratio Math. 44 (2011), 131–141.
• [6] Z. L. Chen, A. W. Wickstead, L-weakly and M-weakly compact operators, Indag. Math. (N.S.) 10(3) (1999), 321–336.
• [7] P. G. Dodds, D. H. Fremlin, Compact operators on Banach lattices, Israel J. Math. 34 (1979), 287–320.
• [8] P. Meyer-Nieberg, Banach Lattices, Universitext, Springer-Verlag, Berlin, 1991.
• [9] A. W. Wickstead, Converses for the Dodds–Fremlin and Kalton–Saab theorems, Math. Proc. Cambridge Philos. Soc. 120 (1996), 175–179.
• [10] W. Wnuk, A note on the positive Schur property, Glasg. Math. J. 31 (1989), 169–172.
• [11] W. Wnuk, Remarks on J. R. Holub’s paper concerning Dunford–Pettis operators, Math. Japon. 38(6) (1993), 1077–1080.
• [12] W. Wnuk, Banach lattices with the weak Dunford–Pettis property, Atti Sem. Mat. Fis. Univ. Modena 42(1) (1994), 227–236.
• [13] W. Wnuk, Banach Lattices with Order Continuous Norms, Polish Scientific Publishers, Warsaw 1999.
• [14] A. C. Zaanen, Riesz Spaces II, North Holland Publishing Company 1983.
• [15] A. C. Zaanen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, Berlin, 1997.