Lipschitz (p,r,s)-integral operators and Lipschitz (p,r,s)-nuclear operators

The ideal of Lipschitz classical p-compact operators and its injective hull

“…Since the article of Farmer and Johnson [8], which deals with a class of Lipschitz operators, the p-summing Lipschitz operators, several authors have studied different classes of Lipschitz operators which, in some sense, extends linear Banach operator ideals (see e.g. [2,5,13]). Moreover, the concept of Lipschitz Banach operator ideals defined between a pointed metric space and a Banach space was introduced in [3], extending the Banach linear operator ideals and there is also the injective hull procedure of Banach Lipschitz operator ideals [3, Definition 2.2] which were introduced to generate "new" Lipschitz Banach operator ideals from previous one, which extends the "procedure" in the case of linear operators.…”

“…In the present paper, we deal with a new class of Lipschitz operator ideals which extend the classical p-compact operators of Fourie and Swart and its injective hull [11,10]. In [5] the notion of Lipschitz ideal of (strongly) Lipschitz (p, r, s)-nuclear operator was introduced and in this article the ideal of (strongly) Lipschitz (∞, p, p * )-nuclear operators will be call (strongly) Lipschitz classical p-compact. The article is organized as follows.…”

“…The article is organized as follows. In Section 2, we introduce and study the injective hull of the Banach ideal of strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space (also, called strongly Lipschitz (∞, p, p * )-nuclear operator ideal, defined in [5]). We prove that the injective hull of strongly Lipschitz classical p-compact coincides with the Lipschitz composition ideal with the injective hull of classical pcompact linear operators.…”

“…Let ( f j ) j be a sequence in X # . Following [5], the sequence ( f j ) j is Lipschitz ω * -p-summable if there is a constant C such that for all n ∈ N and for all x, x ∈ X we have…”

Strongly Lipschitz up-Nuclear Operators

“…In 2012, Chen and Zheng, [4], generalized the concept of p-nuclear operators to Lipschitz situation, where the domain of such operators is a metric space that need not be a normed space, they published "Lipschitz p-integral operators and Lipschitz p-nuclear operators". Belacel and Chen defined and investigated "Lipschitz (p, r, s)-integral operators and Lipschitz (p, r, s)-nuclear operators" [3].…”