An Introduction to Spectral Theory of Bounded Linear Operators in Intuitionistic Fuzzy Pseudo Normed Linear Space

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

• intuitionistic fuzzy pseudo norm
• resolvent
• spectrum
• strongly intuitionistic fuzzy bounded linear operator
• pseudo norm