arXiv Analytics

Sign in

arXiv:math/0307041 [math.FA]AbstractReferencesReviewsResources

Tensor products in the category of topological vector spaces are not associative

Helge Glockner

Published 2003-07-03, updated 2004-04-30Version 2

We show by example that the associative law does not hold for tensor products in the category of general (not necessarily locally convex) topological vector spaces. The same pathology occurs for tensor products of Hausdorff abelian topological groups.

Comments: 7 pages; v2: new version focusses on the real case
Categories: math.FA
Subjects: 46A16, 46A32, 22A05
Related articles: Most relevant | Search more
arXiv:1604.02846 [math.FA] (Published 2016-04-11)
The space $\dot{\mathcal{B}}'$ of distributions vanishing at infinity - duals of tensor products
arXiv:1108.0169 [math.FA] (Published 2011-07-31, updated 2011-12-21)
Continuity of bilinear maps on direct sums of topological vector spaces
arXiv:2505.02200 [math.FA] (Published 2025-05-04)
Automatic boundedness of some operators between ordered and topological vector spaces

Links

Toolbox