# Some Properties of Fuzzy Norm of Linear Operators

Document Type : Research Paper

Authors

1 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Raf- sanjan, Iran

2 Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

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

Abstract

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

Keywords

#### References

bibitem{1}
T. Bag and S. K. Samanta, {\it Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces}, Fuzzy Sets and Systems, {\bf 159} (2008), 685-707.
%\bibitem{2}
%T. Bag, S.K. Samanta, {\it Fuzzy bounded linear operators}, Fuzzy Sets and Systems, {\bf 151} (2005), 513-547.
\bibitem{3}
C. Felbin, {\it Finite dimensional fuzzy normed linear space}, Fuzzy Sets and Systems, {\bf 48} (1992), 239-248.
%\bibitem{4}
%C. Felbin, {\it The completion of a fuzzy normed linear space}, Mathematical Analysis and Applications, {\bf 174} (1993), 428-440.
\bibitem{5}
A. Hasankhani, A. Nazari and M. Saheli, {\it Some properties of fuzzy hilbert spaces and norm of operators}, Iranian Journal of Fuzzy Systems, {\bf 7}\textbf{(3)} (2010), 129-157.
\bibitem{55}
A. Hasankhani, A. Nazari and M. Saheli, {\it Bounded inverse theorem and compact linear operators on fuzzy normed linear spaces}, Ital. J. Pure Appl. Math., accepted for publication.
\bibitem{7}
O. Kaleva and S. Seikkala, {\it On fuzzy metric spaces}, Fuzzy Sets and Systems, {\bf 12} (1984), 215-229.
\bibitem{6}
E. Kreyszig, {\it Introductory functional analysis with applications}, John Wiley and Sons, New York, 1978.
\bibitem{8}
J. Xiao and X. Zhu, {\it Fuzzy normed space of operators and its completeness}, Fuzzy Sets and Systems, {\bf 133} (2003), 389-399.
\bibitem{9}
J. Xiao and X. Zhu, {\it On linearly topological structure and property of fuzzy normed linear space}, Fuzzy Sets and Systems, {\bf 125} (2002), 153-161.