Injective envelopes of real C*- and AW*-algebras
Operator Algebras
2025-02-11 v2
Abstract
It is shown that every outer *-automorphism of a real C*-algebra can be uniquely extended to an injective envelope of real C*-algebra. It is proven that if a real C*-algebra is a simple, then its injective envelope is also simple, and it is a real AW*-factor. The example of a real C*-algebra that is not real AW*-algebra and the injective envelope is a real AW*-factor of type III, which is not a real W*-algebra is constructed. This leads to the interesting result that up to isomorphism, the class of injective real (resp. complex) AW*-factors of type III is at least one larger than the class injective real (resp. complex) W*-factors of type III.
Cite
@article{arxiv.2502.04137,
title = {Injective envelopes of real C*- and AW*-algebras},
author = {A. A. Rakhimov and L. D. Ramazonova},
journal= {arXiv preprint arXiv:2502.04137},
year = {2025}
}