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

Han Wang; Jianrong Wu; Han Wang; Jianrong Wu

doi:10.3934/math.2022655

AIMS Mathematics

2022, Volume 7, Issue 7: 11759-11771. doi: 10.3934/math.2022655

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Research article

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

Han Wang ¹,
Jianrong Wu ^{2
,
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College of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China

Received: 31 December 2021 Revised: 16 March 2022 Accepted: 17 March 2022 Published: 18 April 2022
MSC : 46B28, 46S40

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.
- fuzzy quasi-norm,
- continuous linear operator,
- bounded linear operator,
- family of star quasi-seminorms,
- fuzzy functional analysis
Citation: Han Wang, Jianrong Wu. The norm of continuous linear operator between two fuzzy quasi-normed spaces[J]. AIMS Mathematics, 2022, 7(7): 11759-11771. doi: 10.3934/math.2022655

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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.

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