A note on the concept of factorable strongly p-summing operators

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It is known that an n-homogeneous polynomial is factorable strongly p-summing if and only if its linearization is absolutely p-summing. We prove that a similar result holds for n-linear operators and, as a consequence, we present simplified proofs of recent results from Pellegrino et al. (Rev R Acad Cienc Exactas Fis Nat Ser A Mat RACSAM 110(1):285–302, 2016). Using this connection and the well-known results of the classical linear theory of absolutely p-summing operators we prove other properties for this class of multilinear operators.