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General construction of Banach-Grassmann algebras

Vladimir G. Pestov (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

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