Injective envelopes of real C*- and AW*-algebras

A. A. Rakhimov; L. D. Ramazonova

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arXiv · 2502.04137

Injective envelopes of real C- and AW-algebras

A. A. Rakhimov·L. D. Ramazonova

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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.

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BibTeX RIS

A. A. Rakhimov, L. D. Ramazonova. 2025-02-06. Injective envelopes of real C*- and AW*-algebras. https://arxiv.org/abs/2502.04137

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