Module tensorizing maps on $ C^*$-algebras
Ahmad Shirinkalam

TL;DR
This paper explores the structure of module tensor products of $C^*$-algebras over a common algebra, introducing new concepts like module tensorizing maps and module nuclear pairs, with examples from inverse semigroup algebras.
Contribution
It introduces the notions of module tensorizing maps, module exactness, and module nuclear pairs for $C^*$-algebras, expanding the theory of tensor products in the module setting.
Findings
Established relations between amalgamated module tensor products and standard $C^*$-tensor products.
Defined and analyzed module tensorizing maps and module nuclear pairs.
Provided concrete examples involving $C^*$-algebras on inverse semigroups.
Abstract
For -algebras and where and are -bimodules with compatible actions, we consider amalgamated -module tensor product of and and study its relation with the C*-tensor product of and for the min and max norms. We introduce and study the notions of module tensorizing maps, module exactness, and module nuclear pairs of -algebras in this setting. We give concrete examples of -algebras on inverse semigroups.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra
