Bulletin de la Société Royale des Sciences de Liège

0037-9565 1783-5720

 

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Dietmar VOGT

The Tensor Algebra of the Space s

(Volume 70 - Année 2001 — Numéro 4 - 5 - 6)
Article
Open Access

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.

Om dit artikel te citeren:

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 : http://popups.ulg.be/0037-9565/index.php?id=2298.

Over : Dietmar VOGT

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