Abstract
We introduce the unifying concept of (p, S)-summing operator which include the well-known concept of p-summing operator as well the concept of summing operator introduced by Kislyakov and Blasco-Signes. We prove a Pietsch’s domination theorem and a splitting lemma from which we derive a Pietsch’s composition type result for this new class. The new feature of our splitting result is that the proof is entirely different than those known in the literature.
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We would like to thank the two referees of our paper for carefully reading the manuscript and for such constructive comments, remarks and suggestions which helped improving the first version of the paper.
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Popa, D. The splitting property for \((\,p,S)\)-summing operators. RACSAM 111, 167–175 (2017). https://doi.org/10.1007/s13398-016-0284-4
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DOI: https://doi.org/10.1007/s13398-016-0284-4