Remarks on <i>p</i>-cyclically monotone operators

In this paper, we deal with three aspects of <i>p</i>-cyclically monotone operators. First, we introduce a notion of monotone polar adapted for <i>p</i>-cyclically monotone operators and study these kinds of operators with a unique maximal extension (called pre-maximal), and with a convex graph. We then deal with linear operators and provide characterizations of <i>p</i>-cyclical monotonicity and maximal <i>p</i>-cyclical monotonicity. Finally, we show that the Brézis-Browder theorem preserves <i>p</i>-cyclical monotonicity in reflexive Banach spaces.本文针对*p*-循环单调算子（p-cyclically monotone operators）的三个研究方向展开系统性探讨。首先，本文提出适配于该类算子的单调极（monotone polar）概念，并针对两类特殊的*p*-循环单调算子开展研究：一类具备唯一极大延拓（亦称预极大（pre-maximal）算子），另一类具有凸图像（convex graph）。其次，本文聚焦线性算子，给出*p*-循环单调性与极大*p*-循环单调性的数学刻画。最后，本文证明在自反巴拿赫空间（reflexive Banach spaces）中，布雷斯-布罗德尔定理（Brézis-Browder theorem）可保持*p*-循环单调性。

搜集汇总

背景与挑战

背景概述

该数据集是2019年发表的学术论文'Remarks on p-cyclically monotone operators'的补充材料，主要研究p-cyclically单调算子的理论性质，包括单调极概念、线性算子表征和Brézis-Browder定理的扩展。数据集属于数学科学领域，但涉及生物物理学、医学等多个交叉学科分类，采用CC BY 4.0开放许可协议。