模糊Riesz空间中的模糊算子
Fuzzy Operators in Fuzzy Riesz Spaces
摘要: 本文首先讨论模糊赋范Riesz空间上模糊序连续范数的一些性质，得到模糊序连续范数与模糊范闭理想之间的联系，给出模糊σ-理想的等价命题，然后给出了模糊理想是模糊投影带的必要条件；最后讨论了模糊赋范Riesz空间上模糊序连续算子的一些性质及研究模糊算子扩张，得到模糊序有界正算子构成的模糊理想的性质及模糊理想上的模糊算子与模糊序连续算子之间的关系。
Abstract: In this paper, we first discuss some properties of fuzzy ordered continuous norms on fuzzy normed Riesz spaces such as the relationship between fuzzy ordered continuous norms and fuzzy normed closed ideals, giving the equivalent proposition of fuzzy σ-ideals, and then give the necessary conditions for fuzzy ideals to be fuzzy projective bands. Finally, we discuss some properties of fuzzy ordered continuous operators on fuzzy normed Riesz spaces and study the extension of fuzzy operators. We obtain the properties of fuzzy ideals formed by fuzzy ordered bounded positive operators and the relationship between fuzzy operators on fuzzy ideals and fuzzy ordered continuous operators.
文章引用：赵娟娟, 程娜. 模糊Riesz空间中的模糊算子[J]. 理论数学, 2022, 12(11): 1902-1909. https://doi.org/10.12677/PM.2022.1211204

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