General approach to Köthe echelon algebras

Autor:	Tomasz Ciaś, Krzysztof Piszczek
Rok vydání:	2021
Předmět:	Sequence Pure mathematics General Mathematics 010102 general mathematics Holomorphic function Nuclear space Type (model theory) 01 natural sciences 010101 applied mathematics Character (mathematics) Bimodule 0101 mathematics Algebra over a field Mathematics
Zdroj:	Mathematische Nachrichten. 294:486-517
ISSN:	1522-2616 0025-584X
DOI:	10.1002/mana.201900121
Popis:	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)‐(Ω) 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::096d3a95a64fa2b69655078944c01377 https://doi.org/10.1002/mana.201900121 Zobrazit plný text záznamu Plný text ve formátu PDF