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Applications of ternary rings to $C^*$-algebras by Abadie, Fernando; Ferraro, Damián is a scholarly article available to read on EtoBox.

What is Applications of ternary rings to $C^*$-algebras about?

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its corresponding $*$-algebra. We apply this functor to obtain Morita-Rieffel equivalence results between cross sectional $C^*$-algebras of Fell bundles, and to extend the theory of tensor products of $C^*$-algebras to the larger category of full Hilbert $C^*$-modules. We prove that, like in the case of $C^*$-algebras, there exist maximal and minimal tensor products. As applications we give simple proofs of the invariance of nuclearity and exactness under Morita-Rieffel equivalence of $C^*$-algebras.

Author

Abadie, Fernando; Ferraro, Damián

Published

2016

Language

EN