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- Volume 70 - Année 2001
- Numéro 4 - 5 - 6
- The Tensor Algebra of the Space s
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The Tensor Algebra of the Space s
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Abstract
In view of recent work on non commutative geometry involving various Fréchet spaces (resp. algebras), isomorphic to the space s of rapidly decreasing sequences, and their tensor algebras it appears to be of interest to determine the isomorphy type of the tensor algebra T(s) of s. We show that T(s) s and that, moreover, for any complemented subspace E of s with dim E 2 we have T(s) s. This, in particular, includes all nuclear power series spaces of infinite type as e.g. the space of entire holomorphic functions in any finite dimension.
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A propos de : Dietmar VOGT
Bergische Universität Wuppertal, FB Mathematik, Gaußtr. 20, D-42097 Wuppertal, Germany, dvogt@math.uni-wuppertal.de