Abstract
The aim of this work is to contribute to the theory of \((p,q)\)-summing operators. We focus on positive \((p,q)\)-summing operators, introduced by Blasco (Collect Math 37(1):13–22, 1986). We characterize their conjugates and provide new domination/factorization theorems for these classes. As an application, it is also shown that certain known results on \((p,q)\)-concave operators from Banach lattices can be lifted to a class of \((q,p)\)-convex operators.
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Acknowledgments
This work is a part of the doctoral thesis of A. Belacel. The authors wish to thank Professor E. A. Sánchez Pérez for his many useful suggestions concerning this paper.
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Achour, D., Belacel, A. Domination and factorization theorems for positive strongly \(p\)-summing operators. Positivity 18, 785–804 (2014). https://doi.org/10.1007/s11117-014-0276-6
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DOI: https://doi.org/10.1007/s11117-014-0276-6
Keywords
- Banach lattice
- Positive \((p, q)\)-summing operators
- Pietsch-type theorem
- Strongly \((p, q)\)-summing operators
- Tensor norm