RMC - J. M. F. Castillo/J. A. López Molina

Full paper in PDF:
$%J. M. F. Castillo and J. A. López Molina, Dunford-Pettis-like properties of projective and natural tensor product spaces, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 2, 233–240.%$

Dunford-Pettis-like Properties of Projective and Natural Tensor Product Spaces

Jesús M. F. CASTILLO and Juan A. LÓPEZ MOLINA

Departamento de Matemáticas Universidad de Extremadura Avda. de Elvas, S/N 06071 Badajoz — Spain	Departamento de Matemáticas E.T.S. Ingenieros Agrónomos Camino de Vera, S/N 46022 Valencia — Spain

Received: November 10, 1992
Revised: March 15, 1993

ABSTRACT

Several properties of weakly $p$ -summable sequences and of the scale of $p$ -converging operators (i.e., operators transforming weakly $p$ -summable sequences into convergent sequences) in projective and natural tensor products with an $lp$ space are considered. The last section studies the Dunford-Pettis property of order $p$ (i.e., every weakly compact operator is $p$ -convergent) in those spaces.

1991 Mathematics Subject Classification: 46B20, 46B28, 46B45.