A Note on the Concept of Absolutely \(p\)–summing Operators

This paper presents new insights into the properties of absolutely P-summing operators in Banach space of sequence of operators. Leveraging the classical linear theory of absolutely summing operators, we establish novel characterizations in terms of their representing operator valued measures and provide simplified proofs of recent results. Furthermore, we explore the connections between dominated and absolutely P-summing operators, leading to new applications. Our works helps to unify and extend the understanding of these operator classes with in functional analysis.