The norm of continuous linear operator between two fuzzy quasi-normed spaces

Abstract

In this paper, firstly, we introduce the concepts of continuity and boundedness of linear operators between two fuzzy quasi-normed spaces with general continuous t-norms, prove the equivalence of them, and point out that the set of all continuous linear operators forms a convex cone. Secondly, we establish the family of star quasi-seminorms on the cone of continuous linear operators, and construct a fuzzy quasi-norm of a continuous linear operator.

Keywords

• fuzzy quasi-norm
• continuous linear operator
• bounded linear operator
• family of star quasi-seminorms
• fuzzy functional analysis