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Fuzzy bounded linear operators. (English) Zbl 1077.46059

Summary: A notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types (strong and weak) of fuzzy bounded linear operators are defined. The relation between fuzzy continuity and fuzzy boundedness is studied. Definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed. The Hahn-Banach theorem, the open mapping theorem, the closed graph theorem and the uniform boundedness principle theorem are established.

MSC:

46S40 Fuzzy functional analysis
47S40 Fuzzy operator theory
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