RMC - Vol. 6, Num. 1 - J. M. F. Castillo/F. Sánchez

Full paper in PDF:
$%J. M. F. Castillo and F. Sánchez, Dunford-Pettis-like properties of continuous vector function spaces, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 1, 43–59.%$

Dunford-Pettis-like Properties of Continuous Vector Function Spaces

Jesús M. F. CASTILLO and Fernando SÁNCHEZ

Departamento de Matemáticas
Universidad de Extremadura
Avda. de Elvas, s/n
06071 Badajoz — Spain

Received: December 12, 1991
Revised: March 6, 1992

ABSTRACT

In this paper, the structure of some operator ideals $A$ defined on continuous functions spaces is studied. Conditions are considered under which “ $T (- A$ ” and “the representing measure of $T$ takes values in $A$ ” are equivalent for the scales of p-converging $(Cp)$ and weakly- $p$ -compact $(Wp)$ operators. The scale $Cp$ is intermediate between the ideals $Cl = U$ (unconditionally summing operators) and $C oo = B$ (completely continuous operators), which have been studied by several authors (Bombal, Cembranos, Rodríguez-Salinas, Saab). The dual scale $Wp$ is intermediate between the ideals $K$ (compact operators) and $W = W o o$ (weakly compact operators), and the result presented have a close connection with those of Diestel, Núñez, and Seifert.

1991 Mathematics Subject Classification: 46E15, 46B28, 46B25.