Abstract
For a bounded n-linear operator , , ..., a system of n bounded linear operators and we introduce the concept of Grothendieck–Pietsch -dominated operator. We use Ky-FanLemma to prove a characterization of -dominated operators. As application we characterize -dominated operators on . We show that similar ideas can be used to obtain a new characterization of the dominated operators in the sense of N. Dinculeanu and, as an application, we prove an extension of a result of A. Defant and M. Junge.
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Acknowledgements
We thank the referee for his/her constructive comments and remarks which have improved the first version of this paper.
Notes
No potential conflict of interest was reported by the author.