Fuzzy Hilbert $C^*$-modules

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.

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 Mn(A)-valued fuzzy inner product, where Mn(A) denotes the n × n matrix C∗-algebra of a unital C∗-algebra A. Moreover, we obtain some relations with the notion of C∗-valued fuzzy normed spaces.