Revisiting Operator p-Compact Mappings

Abstract

We continue our study of the mapping ideal of operator p-compact maps, previouslyintroduced by the authors. Our approach embraces a more geometric perspective, delving intothe interplay between operator p-compact mappings and matrix sets, specifically we provide aquantitative notion of operator p-compactness for the latter. In particular, we consider operatorp-compactness in the bidual and its relation with this property in the original space. Also, wedeepen our understanding of the connections between these mapping ideals and other significantones (e.g., completely p-summing, completely p-nuclear).