On some fuzzy hyponormal operators

A. Radharamani; A. Brindha

doi:10.26637/MJM0704/0001

Abstract

In this work,we focus our study on Fuzzy hyponormal operators acting on a fuzzy Hilbert space(FH space).we have given some properties of Fuzzy hyponormal operators on a FH space.And also we introduced the definition of Fuzzy class (N) operator acting on a Fuzzy Banach space (FB-space) and some definitions, theorems are discussed in detail.

Keywords:

Fuzzy Banach Space, Fuzzy Hilbert Space, Fuzzy Normal Operator, Fuzzy Hyponormal Operator, Fuzzy class (N).

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

A. Radharamani Department of Mathematics, Chikkanna Government Arts College, Tirupur-641604, Tamil Nadu, India
A. Brindha Department of Mathematics, Tiruppur Kumaran College for Women, Tirupur-641687, Tamil Nadu, India.

Pages: 607-611
Date Published: 01-10-2019
Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

A. Radharamani, A. Brindha, Fuzzy hyponormal operator in Fuzzy Hilbert space, International Journal of Mathematical Archive (IJMA), 10(1)(2019), 6-12.

A.Radharamani, A.Brindha, S.Maheswari, Fuzzy Normal Operator in fuzzy Hilbert space and its properties, IOSR Journal of Engineering, 8(7)(2018), 1-6.

Sudad.M. Rasheed, Self- adjoint fuzzy operator in fuzzy Hilbert space and its properties, Journal of Zankoy Sulaimani, 19(1)(2017), 233-238.

K.Katsaras, Fuzzy topological vector space-II, Fuzzy Sets and Systems, 12(1984), 143-154.

B. Punnose and S. Kuriakose, Fuzzy inner product spaceA new approach, Journal of Fuzzy Math, 14(2)(2006), $273-282$

C. Felbin, Finite dimensional Fuzzy normed linear space, Fuzzy Sets and Systems, 48(1992), 239-248.

J.K. Kohil and R. Kumar, Linear mappings, Fuzzy linear spaces, Fuzzy inner product spaces and Fuzzy Co- inner product spaces, Bull Calcutta Math. Soc., 87(1995), 237246.

J.K. Kohil and R. Kumar, On fuzzy inner product spaces and fuzzy co- inner product spaces, Bull Calcutta Math.Soc., 53(1993), 227-232.

M. Goudarzi and S.M. Vaezpour, On the definition of fuzzy Hilbert spaces and its applications, J. Nonlinear Sci. Appl., 2(1)(2009), 46-59.

P.Majumdar and S.K.Samanta, On Fuzzy inner product spaces, J.Fuzzy Math., 16(2)(2008), 377-392.

R. Biswas, Fuzzy inner product spaces and Fuzzy norm functions, Information Sciences 53(1991), 185-190.

R.Saadati and S.M.Vaezpoor, Some results on fuzzy Banach spaces, J. Appl. Math. and Computing, 17(1)(2005), $475-488$.

S.C.Cheng, J.N.Mordeson, Fuzzy linear operators and Fuzzy normed linear spaces, Bull. Cal. Math. Soc., $86(1994), 429-436$.

T.Bag, S.K.Samanta, Operators Fuzzy Norm and some properties Fuzzy,Inf. Eng., 7(2015), 151-164.

Yongfusu. Riesz Theorem in probabilistic inner product spaces, Inter. Math. Forum, 2(62)(2007), 3073-3078.

T.Bag, S.K. Samanta, Finite Dimensional fuzzy normed linear spaces, J.Fuzzy Math, 11(3)(2003), 687-705.

G.F.Simmons, Introduction to Topology and Modern Analysis, New Delhi, Tata McGraw-Hill, 1963.

Balmohan V Limaye, Functional Analysis, New Delhi: New Age International, 1996.

Noori F.AI- Mayahi, Abbas M. Abbas, Some properties of spectral theory in fuzzy Hilbert spaces, Journal of AL-Qadisiyah for Computer Science and Mathematics, $8(2)(2016), 1-7$.

V.Istratescu, On Some Hyponormal Operators, Pacific Journal of Mathematics, 22(3)(1967), 413-417.

A. Radharamani, Fuzzy unitary operator in fuzzy Hilbert space and its properties, International Journal of Research and Analytical Reviews (IJRAR), 15(4)(2018), 258261.