We study the pointwise partial ordering of representative functions for a monotone operator and in particular we focus on the bigger conjugate representative functions that represent a fixed initial (non-maximal) monotone operator. The first problem considered is that of constructing a new representative function from a given member of this class when wanting to add an additional monotonically related point. This study allows us to prove that all bigger conjugate representable monotone sets are monotonically closed. This result sheds light on the structure of the domains for maximal monotone operators and enables us to study the sum theorem for FPV operators in Banach spaces which posses a dual space that has a strictly convex renorm.

我们研究了单调算子的代表函数的逐点偏序，特别是我们专注于代表固定的初始（非最大）单调算子的较大共轭代表函数。考虑的第一个问题是，当要添加其他单调相关的点时，从此类的给定成员构造一个新的代表函数。这项研究使我们能够证明所有更大的共轭可表示单调集都是单调封闭的。该结果阐明了最大单调算子的域结构，并使我们能够研究Banach空间中FPV算子的和定理，该定理具有严格凸凸范数的对偶空间。