Classification of locally m-convex algebras through Le Page condition

• Autorzy: Haralampidou M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

locally m-convex algebra; Frechet locally m-convex algebra; division algebra; generalized Le Page condition; semisimple algebra; generalized Le Page (topological) algebra; Q'- algebra; Arens- Michael decomposition

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr 2
• Strony: 255--269
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Haralampidou M.

• Department of Mathematics, University of Athens Panepistimiopolis, Athens 157 84, Greece,

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