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Classification of locally m-convex algebras through Le Page condition

Haralampidou M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 2

255-269

We classify certain locally m-convex algebras, in terms of Le Page condition. In particular, we show that a unital locally m-convex algebra E satisfies Le Page condition and has no non-trivial idempotents if and only if E = C , within a topological algebra isomorphism. Besides, the algebra Cm<-E^ ( pointwise defined operations and cartesian product topology) characterizes all complex unital complete locally m-convex Le Page Q'-algebras E which have a discrete spectrum VJl(E). Hence, the algebra in question is not finite dimensional, by contrast with the classical case, where a unital complex Banach algebra satisfying Le Page condition is finite dimensional. The first principal Wedderburn structure theorem, for certain particular locally m-convex algebras satisfying the generalized Le Page condition is obtained.