Banach lattices with properties of dunford- pettis type
DOI:
https://doi.org/10.22199/S07160917.1995.0001.00006Keywords:
Toeplitz operators, Hankel operators, Wiener-Hopf operatorsAbstract
This paper is devoted to relationships between weakly compact operators and M- weakly compact (L-weakly compact) operators acting from (resp. into) Banach lattices. We define the M - Dunford - Pettis Property for Banach lattices and the L-Dunford-Pettis Property in Banach spaces. The paper contains some characterizations of this two properties.
References
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[2] P. Dodds and H. Fremlin, Compact Operators in Banach Lattices, Israel J. of Math. 34, 278- 320, (1979).
[3] P. Dodds, 0-weakly compact mapping of Riesz spaces, Trans. Amer. Math. Soc. 214,389- 405, (1979).
[4] A. Grothedieck, Sur les applications lineaires faiblement compactes d'espaces du type C(K), Canad. J. of Math. 5, 129- 173, (1953).
[5] P. Meyer- Nieberg, Uber Klassen schwach kompakter operatoren in Bancahverbanden, Math. Z. 138,145- 159, (1974)
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[8] W. Wnuk, Banach lattices with Properties of the Schur type. A Survey, Conference del Seminario di Matematica dell'Universitat di Bari, 249, (1993).
[9] C. Zaanen, Riesz Space 11, North - Holland Publishing Company, Amsterdam-New York-Oxford, (1984).
[2] P. Dodds and H. Fremlin, Compact Operators in Banach Lattices, Israel J. of Math. 34, 278- 320, (1979).
[3] P. Dodds, 0-weakly compact mapping of Riesz spaces, Trans. Amer. Math. Soc. 214,389- 405, (1979).
[4] A. Grothedieck, Sur les applications lineaires faiblement compactes d'espaces du type C(K), Canad. J. of Math. 5, 129- 173, (1953).
[5] P. Meyer- Nieberg, Uber Klassen schwach kompakter operatoren in Bancahverbanden, Math. Z. 138,145- 159, (1974)
[6] J. Sanchez, The Positive Schur Property, Extracta Mathematicae, Vol. 7, Nº- 2- 3, 161- 163, (1992).
[7] H. Schaeffer, Banach Lattices and Positive Operators, Springer Verlag, Berlin-Heidelberg-New York, (1974).
[8] W. Wnuk, Banach lattices with Properties of the Schur type. A Survey, Conference del Seminario di Matematica dell'Universitat di Bari, 249, (1993).
[9] C. Zaanen, Riesz Space 11, North - Holland Publishing Company, Amsterdam-New York-Oxford, (1984).
Published
2018-04-03
How to Cite
[1]
J. A. Sánchez Henríquez, “Banach lattices with properties of dunford- pettis type”, Proyecciones (Antofagasta, On line), vol. 14, no. 1, pp. 65-74, Apr. 2018.
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