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Hasankhani, Abbas, Nazari, Akbar, Saheli, Morteza. (1389). SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS. نشریه علمی دانشگاه سیستان و بلوچستان, 7(3), 129-157. doi: 10.22111/ijfs.2010.196
Abbas Hasankhani; Akbar Nazari; Morteza Saheli. "SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS". نشریه علمی دانشگاه سیستان و بلوچستان, 7, 3, 1389, 129-157. doi: 10.22111/ijfs.2010.196
Hasankhani, Abbas, Nazari, Akbar, Saheli, Morteza. (1389). 'SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS', نشریه علمی دانشگاه سیستان و بلوچستان, 7(3), pp. 129-157. doi: 10.22111/ijfs.2010.196
Hasankhani, Abbas, Nazari, Akbar, Saheli, Morteza. SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS. نشریه علمی دانشگاه سیستان و بلوچستان, 1389; 7(3): 129-157. doi: 10.22111/ijfs.2010.196

SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS

Iranian Journal of Fuzzy Systems
مقاله 10، دوره 7، شماره 3، دی 2010، صفحه 129-157    اصل مقاله (290.32 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2010.196
نویسندگان
Abbas Hasankhani1؛ Akbar Nazari1؛ Morteza Saheli* 2
1Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
2Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
چکیده
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.
کلیدواژه‌ها
Fuzzy norm؛ Fuzzy inner product؛ Fuzzy normed linear space؛ Fuzzy boundedness؛ Strong continuity
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