Anti-C*-algebras
Operator Algebras
2023-12-11 v5
Abstract
We introduce a class of Banach algebras that we call anti-C*-algebras. We show that the normed standard embedding of a C*-ternary ring is the direct sum of a C*-algebra and an anti-C*-algebra. We prove that C*-ternary rings and anti-C*-algebras are semisimple. We give two new characterizations of C*-ternary rings which are isomorphic to a TRO (ternary ring of operators), providing answers to a query raised by Zettl in 1983, and we propose some problems for further study.
Keywords
Cite
@article{arxiv.2305.12273,
title = {Anti-C*-algebras},
author = {Robert Pluta and Bernard Russo},
journal= {arXiv preprint arXiv:2305.12273},
year = {2023}
}
Comments
15 pages. Some typos corrected and some slight notational changes made. Paper has been submitted (Ignore version 4; the wrong file was uploaded)