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Structure of locally idempotent algebras. (English) Zbl 1129.46037
Summary: It is shown that every locally idempotent (locally m-pseudoconvex) Hausdorff algebra A with pseudoconvex von Neumann bornology is a regular (respectively, bornological) inductive limit of metrizable locally m-(k B -convex) subalgebras A B of A. In the case where A, in addition, is sequentially A -complete (sequentially advertibly complete), then every subalgebra A B is a locally m-(k B -convex) Fréchet algebra (respectively, an advertibly complete metrizable locally m-(k B -convex) algebra) for some k B (0,1]. Moreover, for a commutative unital locally m-pseudoconvex Hausdorff algebra A over with pseudoconvex von Neumann bornology, which at the same time is sequentially A -complete and advertibly complete, the statements (a)–(j) of Proposition 3.2 are equivalent.
MSC:
46H05General theory of topological algebras
46H20Structure and classification of topological algebras