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算子的模糊范数及其空间性态的刻画 被引量:1

The Fuzzy Norm of Operators and Description of Properties of Their Space
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摘要 利用模糊分解原理提出模糊赋范线性空间上算子的模糊范数的定义,指出赋此范数的模糊有界线性算子集构成模糊赋范线性空间且保持值域空间的完备性. A new definition of fuzzy norm of linear operators on a fuzzy normed space is introduced. It is showed that the set of fuzzy bounded linear operators endowed with the new fuzzy norm is still a fuzzy normed space and preserves the completeness of their range.
作者 肖建中
出处 《西南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2003年第3期347-351,共5页 Journal of Southwest China Normal University(Natural Science Edition)
基金 江苏省教育厅自然科学基金项目(02KJD110007).
关键词 模糊赋范线性空间 模糊有界算子 模糊范数 空间性态 完备性 fuzzy normed linear space fuzzy bounded operator fuzzy norm of operator completeness.
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参考文献4

  • 1Felbin C. Finite dimensional fuzzy normed linear space [J]. Fuzzy Sets and Systems, 1992. 48: 239-248.
  • 2Kaleva O, Seikkala S. On fuzzy metric space [J]. Fuzzy Sets and Systems, 1984, 12: 215-229.
  • 3Xiao Jianzhong, Zhu Xinghua. On linearly topological structure and property of fuzzy normed linear space [J]. Fuzzy sets and Systems,2002, 125: 153-161.
  • 4Wu Congxin, Wu Cong. The supremum and infimum of the set of fuzzy numbers and its application [J]. J Math Anal Appl, 1997,210:499 - 511.

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