Tensor topologies on spaces of symmetric tensor products



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Ansemil, José María M. and Ponte, Socorro (2006) Tensor topologies on spaces of symmetric tensor products. Note di Matematica, 25 (1). pp. 35-47. ISSN 1123-2536

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Official URL: http://siba-ese.unisalento.it/index.php/notemat/article/view/1044/868


Here we show how, in the general context of locally convex spaces, it is possible to get an n-tensor topology (on spaces of n-tensor products) from an n-tensor topology on
spaces of symmetric n-tensors products. Indeed, given an n-tensor topology on the spaces of symmetric n-tensor products we construct an n-tensor topology on the spaces of all n-tensor products whose restriction to the symmetric ones gives the original topology. Moreover, we prove that when one starts with an n-tensor topology, restricts it to symmetric tensors and
then extends it, the original topology is obtained when it is symmetric, and we also obtain
some results on complementation with applications to spaces of polynomials. Part of these
results generalize to the context of locally convex spaces some Floret's results in [17] and [18].

Item Type:Article
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Dedicated to the memory of Klaus Floret (1941-2002)

Uncontrolled Keywords:Tensor product, symmetric tensor topology, locally convex space.
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Topology
ID Code:22570
Deposited On:25 Jul 2013 10:17
Last Modified:10 Aug 2018 09:04

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