Open AccessThe norm of continuous linear operator between two fuzzy quasi-normed spaces
Author(s) -
Han Wang,
Jianrong Wu
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022655
Subject(s) - mathematics , operator norm , continuous linear operator , linear operators , norm (philosophy) , equivalence (formal languages) , operator (biology) , pure mathematics , normed vector space , linear map , operator theory , regular polygon , fuzzy logic , discrete mathematics , mathematical analysis , computer science , biochemistry , chemistry , geometry , repressor , artificial intelligence , political science , transcription factor , law , bounded function , gene
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.