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

Shirinkalam, Ahmad

doi:10.22060/ajmc.2025.24545.1437

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

Articles in Press

Document Type : Original Article

Author

Ahmad Shirinkalam ¹^{, 2}

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

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

Exact semigroup

Subjects