2023/05/20 by Robert Pluta, Pluta, Robert, Bernard Russo +1
Computer Science · Mathematics · #16S99 #46H25 #46L08 #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2305.12273
openalex publication_date 2023/05/20 · openalex created_date 2023/05/24 · openalex updated_date 2026/07/28
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.