Abstract
In this paper, we provide an abstract approach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is to unify the study of several known classes and results, for example multiple $$(p, q_1,\ldots , q_n)$$ -summing operators, multiple mixing (s, q, p)-summing operators and multiple strong (s, q, p)-mixing summing operators. We define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper.
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