Cohen positive strongly p-summing and p-convex multilinear operators

On the positive Dimant strongly $p$-summing multilinear operators

“…In this way, our objective is to extend the concept of Dimant strongly p-summing multilinear operators to positive framework, also to study its ties with other known classes of summability. On the other hand, this work presents a continuation of the article [3].…”

“…For example, V. Dimant in [6] defined the concept of strongly p-summing multilinear operators. Next, D. Achour and L. Mezrag in [2] introduced and studied the new notion called Cohen strongly p-summing multilinear operators, this last notion was extended by D. Achour and A. Belacel to the positive linear case (see [1]) and, by A. Bougoutaia and A. Belacel to the positive multilinear case (see [3]). In this way, our objective is to extend the concept of Dimant strongly p-summing multilinear operators to positive framework, also to study its ties with other known classes of summability.…”

Domination and Kwapień’s factorization theorems for positive Cohen p–nuclear m–linear operators

“…By Pietsch's domination theorem for Cohen positive strongly p−summing m−linear operator [7,Theorem 2.5], T ∈ D m+ p (E 1 , ..., E m ; F) and d m+ p (T) ≤ n m+ p (T) .…”

“…2) If T is positive Cohen p−nuclear. Then, T ∈ D m+ p (E 1 , ..., E m ; F) and we have by [7,Proposition 3.3], T ∈ C vex, mult p (E 1 , ..., E m ; F) .…”

“…Now, we continue in specifying definition of the Cohen positive strongly p−summing m−linear operators and the positive multiple p−summing were introduced in [7], [10] respectively. Definition 1.1 [7] Let 1 ≤ p ≤ +∞. An m−linear operator T :…”