SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

Abstract

In the present paper we define the notion of fuzzy inner product
and study the properties of the corresponding fuzzy norm. In particular, it is
shown that the Cauchy-Schwarz inequality holds. Moreover, it is proved 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.
Finally, the notions of fuzzy boundedness and operator norm are introduced
and the relationship between continuity and boundedness are investigated. It
is shown also that the space of all fuzzy bounded operators is complete.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 7, Issue 3 - Serial Number 3
September and October 2010
Pages 129-157

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