Banach lattices with properties of dunford- pettis type

Authors

  • José A. Sánchez Henríquez Universidad de Concepción.

DOI:

https://doi.org/10.22199/S07160917.1995.0001.00006

Keywords:

Toeplitz operators, Hankel operators, Wiener-Hopf operators

Abstract

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.

Author Biography

José A. Sánchez Henríquez, Universidad de Concepción.

Departamento de Métodos Matemáticos, Facultad de Ciencias Físicas y Matemáticas.

References

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[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.

Issue

Section

Artículos