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General approach to Kothe echelon algebras

机译：Kothe Echelon代数的一般方法

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摘要

We provide a study of Kothe sequence algebras. These are Frechet sequence algebras which can be viewed as abstract analogoues of algebras of smooth or holomorphic functions. Of particular treatment are the following properties: unitality, m-convexity, Q-property and variants of amenability. These properties are then checked against the topological (DN)-(Omega) type conditions of Vogt-Zaharjuta. Description of characters and closed ideals in Kothe echelon algebras is provided. We show that these algebras are functionally continuous and we characterize completely which of them factor. Moreover, we prove that closed subalgebras of Montel m-convex Kothe echelon algebras are Kothe echelon algebras as well and we give a version of Stone-Weiestrass theorem for these algebras. We also emphasize connections with the algebra of smooth operators.
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