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**Fuzzy normed space of operators and its completeness.**
*(English)*
Zbl 1032.46096

Summary: A new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced and the boundedness of such an operator is described. Furthermore, the space of all bounded linear operators endowed with this fuzzy norm is studied; consequently, its topological structure as well as completeness is given, and that it can itself be made into a fuzzy normed linear space is also shown.

### MSC:

46S40 | Fuzzy functional analysis |

### Keywords:

fuzzy analysis; fuzzy topology; fuzzy normed linear space; fuzzy norm of operator; boundedness; completeness
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\textit{J. Xiao} and \textit{X. Zhu}, Fuzzy Sets Syst. 133, No. 3, 389--399 (2003; Zbl 1032.46096)

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### References:

[1] | Felbin, C., Finite dimensional fuzzy normed linear space, Fuzzy sets and systems, 48, 239-248, (1992) · Zbl 0770.46038 |

[2] | Kaleva, O.; Seikkala, S., On fuzzy metric space, Fuzzy sets and systems, 12, 215-229, (1984) · Zbl 0558.54003 |

[3] | Kelley, J.L.; Namioka, I., Linear topological spaces, (1976), Springer New York, Heidelberg, Berlin |

[4] | Schechter, M., Principles of functional analysis, (1971), Academic Press New York, London · Zbl 0211.14501 |

[5] | Wu, C.X.; Wu, C., The supremum and infimum of the set of fuzzy numbers and its application, J. math. anal. appl., 210, 499-511, (1997) · Zbl 0883.04008 |

[6] | Xiao, J.; Zhu, X., On linearly topological structure and property of fuzzy normed linear space, Fuzzy sets and systems, 125, 153-161, (2002) · Zbl 1018.46039 |

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