Domination and factorization theorems for positive strongly $$p$$ p -summing operators

Bu’s theorem in the positive situation

“…Then F) . By Pietsch's domination theorem [1,Proposition 3.4] there exists a probability measure µ on the set B + n 2 provided with the weak * topology, and a constant C > 0, such that for any…”

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

“…We present now the main result, Kwapień's Factorization Theorem, of this section. For the proof, we will use the following lemma due to D. Achour and A. Belacel, see [2,Lemma 3.5]. For more informations about J p,0 and L p 0 (µ), see [2, p792-793].…”

“…The class of all positive strongly p−summing operators between X and F is denoted by D + p (X, F) (see [2]). The infimum of all the constant C in the inequality (1.4) defines a norm…”

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

“…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.…”

“…. , E m , F, G will be Banach lattices over K = R or C. Let 1 ≤ p ≤ ∞, and p * is the conjugate of p, i.e., 1 p + 1 p * = 1. We write X * to denote the topological dual of X.…”