Abstract
We show that any hermitian $^{\ast}$-$l.m.c.a.$, the set of positive elements of which is a locally bounded cone, is necessarily a $Q$-algebra (the converse is not true). We also obtain that the algebra of complex numbers is the unique locally $C^{\ast}$-algebra without zero-divisors.
Citation
A. El Kinani. M. A. Nejjari. M. Oudadess. "On classifying involutive locally $m$-convex algebras, via cones." Bull. Belg. Math. Soc. Simon Stevin 13 (4) 681 - 687, December 2006. https://doi.org/10.36045/bbms/1168957344
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