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.
Banach sequence spaces ideals of multilinear operators multiple summing operators
Mathematics Subject Classification
46B45 47L22 40Bxx
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The authors are very indebted to Geraldo Botelho, whose insightful suggestions helped to improve the paper.
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