Infinite-dimensional Grassmann-Banach algebras
V. D. Ivashchuk
Abstract
A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over K = R with l1-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field K with l1-norm and set of generators of arbitrary power. Any l1-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain l1-space. In non-Archimedean case there exists another possibility for constructing of IDGBA using the Grassmann-Banach functor of injective type.
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