AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

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

Document Type : Original Article

Author
Ahmad Shirinkalam 1, 2
1 Department of Mathematics, CT.C, Islamic Azad University, Tehran, Iran
2 Institute of Cognitive Computational Science, CT.C, Islamic Azad University, Tehran, Iran
10.22060/ajmc.2025.24545.1437
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.
Keywords
Module tensor product
Module tensorizing map
Module nuclear $C^*$-algebra
Module exact $C^*$-algebra
Subjects
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AUT Journal of Mathematics and Computing
Volume 7, Issue 4
Autumn 2026
Pages 479-491