some properties of fuzzy hilbert spaces and norm of operators

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abstract

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define the notion of fuzzy inner product and study the properties of the corresponding fuzzy norm. in particular, we show that the cauchy-schwarz inequality holds. moreover, we prove that every such fuzzy inner product space can be imbedded in a complete one and that every subspace of a fuzzy hilbert space has a complementary subspace.

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document type: thesis

وزارت علوم، تحقیقات و فناوری - دانشگاه شهید باهنر کرمان - دانشکده ریاضی و کامپیوتر

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