Tensor products in the category of topological vector spaces are not associative
Tensor products in the category of topological vector spaces are not associative
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.
7 pages; v2: new version focusses on the real case
Mathematics - Functional Analysis, topological tensor product, associative law, 46A16, 46A32, 22A05, Structure of general topological groups, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), FOS: Mathematics, Spaces of linear operators; topological tensor products; approximation properties, non-locally convex space, Functional Analysis (math.FA)
Mathematics - Functional Analysis, topological tensor product, associative law, 46A16, 46A32, 22A05, Structure of general topological groups, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), FOS: Mathematics, Spaces of linear operators; topological tensor products; approximation properties, non-locally convex space, Functional Analysis (math.FA)
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