SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS

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HASANKHANI A.; NAZARI AKBAR; SAHELI M.

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Journal: Iranian Journal of Fuzzy Systems Year:2010 | Volume:7 | Issue:3 Page(s): 129-157

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Title

SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS

Author(s)

HASANKHANI A. | NAZARI AKBAR | SAHELI M. | Issue Writer Certificate

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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.

Cites

FINITE DIMENSIONAL GENERATING SPACES OF QUASI-NORM FAMILY

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APA: Copy

HASANKHANI, A., NAZARI, AKBAR, & SAHELI, M.. (2010). SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS. IRANIAN JOURNAL OF FUZZY SYSTEMS, 7(3), 129-157. SID. https://sid.ir/paper/573094/en

Vancouver: Copy

HASANKHANI A., NAZARI AKBAR, SAHELI M.. SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2010;7(3):129-157. Available from: https://sid.ir/paper/573094/en

IEEE: Copy

A. HASANKHANI, AKBAR NAZARI, and M. SAHELI, “SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 7, no. 3, pp. 129–157, 2010, [Online]. Available: https://sid.ir/paper/573094/en

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