General construction of Banach-Grassmann algebras
Pestov, Vladimir G.
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 3 (1992), p. 223-231 / Harvested from Biblioteca Digitale Italiana di Matematica
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We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.

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.

Publié le : 1992-09-01
@article{RLIN_1992_9_3_3_223_0,
     author = {Vladimir G. Pestov},
     title = {General construction of Banach-Grassmann algebras},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {3},
     year = {1992},
     pages = {223-231},
     zbl = {0745.46050},
     mrnumber = {1186918},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1992_9_3_3_223_0}
}

Pestov, Vladimir G. General construction of Banach-Grassmann algebras. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 3 (1992) pp. 223-231. http://gdmltest.u-ga.fr/item/RLIN_1992_9_3_3_223_0/

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