Document Type : Research Paper

Authors

1 Department of Mathematics, Mahishamuri Ramkrishna Vidyapith, Howrah 711401, WB, India and Department of Mathematics, Kazi Nazrul University, Asansol 713340, WB, India

2 Department of Mathematics, Kazi Nazrul University, Asansol 713340, WB, India.

3 Department of Mathematics, Uluberia College, Howrah 711315, WB, India

Abstract

In this paper, focus is on the study of spectrum and the spectral properties of bounded linear operators in intuitionistic fuzzy pseudo normed linear spaces(IFPNLS). It is done by studying regular value, resolvent set, spectrum of a linear operator in IFPNLS. Also, some properties of spectrum and resolvent of strongly intuitionistic fuzzy bounded(IFB) linear operators in IFPNLS are being developed. It is observed that, for a linear operator $P$ in an IFPNLS, the resolvent set $\rho(P)$ and spectrum $\sigma(P)$ are nonempty, $\rho(P)$ is open and $\sigma(P)$ is closed set.

Keywords

[1] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), pp. 87-96.
[2] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear space, J. Fuzzy Math., 11 (2003), pp. 687-705.
[3] T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst., 151 (2005), pp. 513-547.
[4] S.C. Cheng and J.N. Mordeson, Fuzzy Linear Operators and Fuzzy Normed Linear Spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429-436. 
[5] B. Dinda, S.K. Ghosh and T.K. Samanta, Intuitionistic fuzzy pseudo normed linear spaces, New Math. Nat. Comput., 15 (2019), pp. 113-127.
[6] B. Dinda, S.K. Ghosh and T.K. Samanta, On w-Convergence and s-Convergence in intuitionistic fuzzy pseudo normed linear spaces, New Math. Nat. Comput., 17(3), (2021), pp. 623-632.
[7] B. Dinda, S.K. Ghosh and T.K. Samanta, Relations on continuities and boundedness in intuitionistic fuzzy pseudo normed linear spaces, South East Asian J. of Mathematics and Mathematical Sciences, 17(3), (2021), pp. 15-30.
[8] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst., 48 (1992), pp. 239-248.
[9] I. Golet, On generalized fuzzy normed spaces and coincidence fixed point theorems, Fuzzy Sets Syst., 161 (2010), pp. 1138-1144.
[10] A.K. Katsaras, Fuzzy topological vector spaces I, Fuzzy Sets Syst., 6 (1981), pp. 85-95.
[11] A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets Syst., 12 (1984), pp. 143-154.
[12] E. Kreyszig, Introductory functional analysis with applications, John Wiley & Sons, New York-London-Sydney, 1978. 
[13] S. Nu adu aban, Fuzzy pseudo-norms and fuzzy F-spaces, Fuzzy Sets Syst., 282 (2016), pp. 99-114.
 
[14] R. Saadati and J.H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), pp. 331-344.
[15] A. Samee A., A. Jameel K. and F. Ali C., Spectral theory in fuzzy normed spaces, Al-Nahrain Journal of Science, 14(2), (2011), pp. 178-185.
[16] H.H. Schaefer and M.P. Wolff, Topological Vector Spaces, Graduate Texts in Mathematics, Springer-Verlag, New York, 1999.
[17] J.Z. Xiao and X.H. Zhu, On linearly topological structures and property of fuzzy normed linear space, Fuzzy Sets Syst., 125 (2002), pp. 153-161.
[18] L.A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), pp. 338-353.