Bulletin de la Société Royale des Sciences de Liège Bulletin de la Société Royale des Sciences de Liège -  Volume 70 - Année 2001  Numéro 4 - 5 - 6 

The Tensor Algebra of the Space s

Dietmar VOGT, 

Bergische Universität Wuppertal, FB Mathematik, Gaußtr. 20, D-42097 Wuppertal, Germany, dvogt@math.uni-wuppertal.de

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.

Pour citer cet article

Dietmar VOGT, «The Tensor Algebra of the Space s», Bulletin de la Société Royale des Sciences de Liège [En ligne], Numéro 4 - 5 - 6, Volume 70 - Année 2001, 435 - 440 URL : https://popups.uliege.be/0037-9565/index.php?id=2298.