Applications of ternary rings to $C^*$-algebras
Operator Algebras
2021-08-12 v1
Abstract
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 -norms on the ternary ring and its corresponding -algebra. We apply this functor to obtain Morita-Rieffel equivalence results between cross sectional -algebras of Fell bundles, and to extend the theory of tensor products of -algebras to the larger category of full Hilbert -modules. We prove that, like in the case of -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 -algebras.
Keywords
Cite
@article{arxiv.1612.08476,
title = {Applications of ternary rings to $C^*$-algebras},
author = {Fernando Abadie and Damián Ferraro},
journal= {arXiv preprint arXiv:1612.08476},
year = {2021}
}