Adjoint Operator In Fuzzy Normed Linear Spaces

Abstract

In this paper, the definition adjoint of the operator on fuzzy normed linear spaces is introduced. It is shown that if \((X, \|\| )\) and \((Y ,\|\|^\sim )\) are two fuzzy normed linear spaces and \(T : X \rightarrow Y\) be a strongly (weakly) fuzzy bounded linear operator, then \(T^*: Y^*\rightarrow X^*\) (adjoint of \(T\) ) is strongly ( weakly) fuzzy bounded linear operator and \(\|T\|^*_\alpha=\|T^*\|^*_\alpha\), for each \(\alpha\in (0,1]\).