Abstract
In the present paper, we introduce a new concept of positive p-majorizing operators as a dual notion of positive p-summing operators and generalize the concept of majorizing operators introduced by Schaefer (Isr J Math 13:400–415, 1972). We introduce the concept of positive (p, q)-dominated operators and prove a positive version of the famous Kwapień’s factorization theorem for (p, q)-dominated operators via positive p-majorizing operators. We also introduce the notion of disjoint p-summing operators which is a new larger class of operators than positive p-summing operators and use it to characterize the Radon–Nikodým property. Finally, we investigate the maximal properties of these four classes of operators and prove that they are maximal in corresponding sense.
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Dongyang Chen was supported by the National Natural Science Foundation of China (Grant No. 11971403) and the Natural Science Foundation of Fujian Province of China (Grant No. 2019J01024).
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Chen, D., Belacel, A. & Chávez-Domínguez, J.A. Positive p-summing operators and disjoint p-summing operators. Positivity 25, 1045–1077 (2021). https://doi.org/10.1007/s11117-020-00798-y
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DOI: https://doi.org/10.1007/s11117-020-00798-y
Keywords
- Positive p-summing operators
- Positive p-majorizing operators
- Positive (p, q)-dominated operators
- Disjoint p-summing operators