Module version of tensorizing maps and tensor products on $C^*$-algebras

Articles in Press

Document Type : Original Article

Author

1 Department of Mathematics, CT.C, Islamic Azad University, Tehran, Iran

2 Institute of Biosocial and Quantum Science and Technologies, CT.C, Islamic Azad University, Tehran, Iran

Abstract

For $C^*$-algebras $\mathfrak{A}, A$ and $B$ where $A$ and $B$ are $\mathfrak{A}$-bimodules with compatible actions, we consider amalgamated $\mathfrak{A}$-module tensor product of $A$ and $B$ and study its relation with the $C^*$-tensor product of $A$ and $B$ for the min and max norms. We introduce and study the notions of module tensorizing maps, module exactness, and module nuclear pairs of $C^*$-algebras in this setting. We illustrate our results for the concrete examples of $C^*$-algebras on inverse semigroups.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 30 December 2025

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