Dominated n-linear operators with respect to a system of n bounded linear operators

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.

Keywords:

• p-summing operators
• Ky Fan lemma
• dominated operators
• operators on spaces of vector valued continuous functions

AMS Subject Classifications:

• Primary: 47L20
• 46G25
• 47H60
• Secondary: 47B10
• 46G10

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.