Fuzzy Hilbert $C^*$-modules
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In the present article, we introduce and study the notion of fuzzy inner product $A$-module, where $A$ is an arbitrary unital $C^*$-algebra. Moreover, we construct some examples of particular classes of $C^*$-algebras. As an application, we obtain some $M_{n}(A)$-valued fuzzy inner product, where $M_{n}(A)$ denotes the $n \times n$ matrix $C^*$-algebra of a unital $C^*$-algebra $A.$ Moreover, we obtain some relations with the notion of $C^*$-valued fuzzy normed spaces.
Abstract
In the present article, we introduce and study the notion of fuzzy inner product $A$-module, where $A$ is an arbitrary unital $C^*$-algebra. Moreover, we construct some examples of particular classes of $C^*$-algebras. As an application, we obtain some $M_{n}(A)$-valued fuzzy inner product, where $M_{n}(A)$ denotes the $n \times n$ matrix $C^*$-algebra of a unital $C^*$-algebra $A.$ Moreover, we obtain some relations with the notion of $C^*$-valued fuzzy normed spaces.