G-Fuzzy Operator Norm

Abstract

In our previous paper, it is shown that topology of [Formula: see text]-fuzzy normed linear space is generated by two types of open balls: one is elliptic and the other is circular. In the theoretical aspect of functional analysis, will this type of exception happen or not? To address this problem in this paper, firstly, [Formula: see text]-fuzzy bounded linear operators as well as [Formula: see text]-fuzzy bounded linear functionals are defined which are the key elements of functional analysis. Then, operator [Formula: see text]-fuzzy norms are introduced for both the cases using the idea of quasi-[Formula: see text]-norm family. The definition of operator [Formula: see text]-fuzzy norm is quite different from the existing operator fuzzy norm. Completeness of operator [Formula: see text]-fuzzy norm is investigated. Lastly, Hahn-Banach theorem in [Formula: see text]-fuzzy setting is studied using all the above concepts.