Castillo, Jesús M. F.; Sánchez, Fernando Dunford-Pettis-like properties of continuous vector function spaces. (English) Zbl 0807.46033 Rev. Mat. Univ. Complutense Madr. 6, No. 1, 43-59 (1993). Summary: The structure of some operator ideals \({\mathfrak A}\) defined on continuous function spaces is studied. Conditions are considered under which “\(T\in {\mathfrak A}\)” and “the representing measure of \(T\) takes values in \({\mathfrak A}\)” are equivalent for the scales of \(p\)-converging \((C_ p)\) and weakly-\(p\)-compact \((W_ p)\) operators. The scale \(C_ p\) is intermediate between the ideals \(C_ 1={\mathfrak U}\) (unconditionally summing operators), and \(C_ \infty={\mathfrak B}\) (completely continuous operators), which have been studied by several authors (Bombal, Cembranos, Rodríguez-Salinas, Saab). The dual scale \(W_ p\) is intermediate between the ideals \(\mathfrak K\) (compact operators) and \(W_ \infty =W\) (weakly compact operators), and the results presented have a close connection with those of Diestel, Núñez and Seifert. Cited in 2 ReviewsCited in 30 Documents MSC: 46E40 Spaces of vector- and operator-valued functions 47L20 Operator ideals 46B28 Spaces of operators; tensor products; approximation properties 46E15 Banach spaces of continuous, differentiable or analytic functions 46B25 Classical Banach spaces in the general theory Keywords:operator ideals defined on continuous function spaces; scales of \(p\)- converging and weakly-\(p\)-compact operators PDFBibTeX XMLCite \textit{J. M. F. Castillo} and \textit{F. Sánchez}, Rev. Mat. Univ. Complutense Madr. 6, No. 1, 43--59 (1993; Zbl 0807.46033) Full Text: EuDML