Pestov: General construction of Banach-Grassmann algebras

Pestov, Vladimir G.:
General construction of Banach-Grassmann algebras (Costruzione generale di algebre di Banach-Grassmann)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 3 (1992), fasc. n.3, p. 223-231, (English)
pdf (1.09 MB), djvu (238 Kb). | MR1186918 | Zbl 0745.46050

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Si mostra che un'algebra di Banach libera graduato-commutativa su uno spazio di Banach \( E \) puramente dispari è un'algebra di BanachGrassmann nel senso di Jadczyk e Pilch se e solo se \( E \) ha dimensione infinita. É quindi possibile ottenere un gran numero di nuovi esempi di algebre di Banach-Grassmann separabili, in aggiunta all'unico esempio precedentemente noto, dovuto ad A. Rogers.

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