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.

在本论文中，我们引入正的新概念p -majorizing运营商为阳性的双概念p -summing运营商和概括majorizing由谢弗引入运营商的概念（ISRĴ数学13：400-415，1972）。我们采用积极的（概念p，  q）-dominated运营商，并证明了著名Kwapień的分解定理（的积极版本p，  q通过正）-dominated运营商p -majorizing运营商。我们还介绍了不相交的p-求和运算符的概念，它是一个比正p大的新运算符。求和运算符，并使用它来表征Radon–Nikodým属性。最后，我们研究了这四种算子的最大性质，并证明它们在相应的意义上是最大的。