On classifying involutive locally $m$-convex algebras, via cones
El Kinani, A. ; Nejjari, M. A. ; Oudadess, M.
Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, p. 681-687 / Harvested from Project Euclid
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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.
Publié le : 2006-12-14
Classification:  $m$-convex algebra,  hermitian algebra,  $Q$-algebra,  locally bounded cone,  zero-divisors,  46H05,  46K05 
@article{1168957344,
     author = {El Kinani, A. and Nejjari, M. A. and Oudadess, M.},
     title = {On classifying involutive locally $m$-convex algebras, via cones},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {12},
     number = {5},
     year = {2006},
     pages = { 681-687},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1168957344}
}

El Kinani, A.; Nejjari, M. A.; Oudadess, M. On classifying involutive locally $m$-convex algebras, via cones. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp.  681-687. http://gdmltest.u-ga.fr/item/1168957344/