Abstract
AbstractWe 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 (Adv Math 48(2): 117–143, 1983), and we propose some problems for further study.
Publisher
Springer Science and Business Media LLC
Reference17 articles.
1. Abadie, F., Ferraro, D.: Applications of ternary rings to C*-algebras. Adv. Oper. Theory 2(3), 293–317 (2017). https://doi.org/10.22034/aot.1612-1085
2. Bunce, L.J., Timoney, R.M.: On the universal TRO of a JC*-triple, ideals and tensor products. Q. J. Math. 64(2), 327–340 (2013). https://doi.org/10.1093/qmath/has011
3. Chu, C.-H., Mellon, P.: JB*-triples have Pelczynski’s Property V. Manuscripta Math. 93(3), 337–347 (1997). https://doi.org/10.1007/BF02677475
4. Ghez, P., Lima, R., Roberts, J.E.: W*-categories. Pacific J. Math. 120(1), 79–109 (1985)
5. Hamana, M.: Triple envelopes and šilov boundaries of operator spaces. Math. J. Toyama Univ. 22, 77–93 (1999)