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arXiv · 2305.12273

Anti-C*-algebras

Robert Pluta·Bernard Russo
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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.

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Robert Pluta, Bernard Russo. 2023-05-20. Anti-C*-algebras. https://arxiv.org/abs/2305.12273

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