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2007 Structure of locally idempotent algebras
Mati Abel
Banach J. Math. Anal. 1(2): 195-207 (2007). DOI: 10.15352/bjma/1240336216


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 $\mathcal{B}_A$-complete (sequentially advertibly complete), then every subalgebra $A_B$ is a locally $m$-($k_B$-convex) Frechet algebra (respectively, an advertibly complete metrizable locally $m$-($k_B$-convex) algebra) for some $k_B\in (0,1]$. Moreover, for a commutative unital locally $m$-pseudoconvex Hausdorff algebra $A$ over $\mathbb{C}$ with pseudoconvex von Neumann bornology, which at the same time is sequentially $\mathcal{B}_A$-complete and advertibly complete, the statements (a)-(j) of Proposition 3.2 are equivalent.


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Mati Abel. "Structure of locally idempotent algebras." Banach J. Math. Anal. 1 (2) 195 - 207, 2007.


Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1129.46037
MathSciNet: MR2366101
Digital Object Identifier: 10.15352/bjma/1240336216

Primary: 46H05
Secondary: 46H20

Keywords: advertibly complete algebras , bornological inductive limit , locally idempotent algebras , locally m-convex algebras , locally m-pseudoconvex algebras , Mackey complete algebras , Mackey Q-algebra , ocally m-(k-convex) algebras , pseudoconvex von Neumann bornology

Rights: Copyright © 2007 Tusi Mathematical Research Group

Vol.1 • No. 2 • 2007
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