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

Helge Glöckner

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 607-614
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Glöckner, Helge. "Tensor products in the category of topological vector spaces are not associative." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 607-614. <http://eudml.org/doc/249357>.

@article{Glöckner2004,
abstract = {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.},
author = {Glöckner, Helge},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological tensor product; associative law; non-locally convex space; topological tensor product; associative law; non-locally convex space},
language = {eng},
number = {4},
pages = {607-614},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Tensor products in the category of topological vector spaces are not associative},
url = {http://eudml.org/doc/249357},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Glöckner, Helge
TI - Tensor products in the category of topological vector spaces are not associative
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 607
EP - 614
AB - 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.
LA - eng
KW - topological tensor product; associative law; non-locally convex space; topological tensor product; associative law; non-locally convex space
UR - http://eudml.org/doc/249357
ER -

References

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  14. Turpin Ph., Produits tensoriels d'espaces vectoriels topologiques, Bull. Soc. Math. Fr. 110 (1982), 3-13. (1982) Zbl0494.46061MR0662126
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