Banach Ideals of Operators Defined by Classes of Cone Absolutely Summing and Strongly Majorizing Mappings

摘要

The ideals of absolutely delta summing and dual absolutely delta summing mappings are characterized as 'quotients' by continuous linear mappings of certain classes of cone absolutely summing and strongly majorizing mappings respectively. The ideals of delta nuclear and right delta nuclear maps are also characterized as products of these two classes of operators with the class of continuous linear mappings. Two propositions are presented which suggest a way of generalizing the notions of absolutely delta summing and delta nuclear mappings.