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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. 3547. ISSN 11232536

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Official URL: http://sibaese.unisalento.it/index.php/notemat/article/view/1044/868
URL  URL Type 

http://sibaese.unisalento.it/index.php/notemat/  Organisation 
Abstract
Here we show how, in the general context of locally convex spaces, it is possible to get an ntensor topology (on spaces of ntensor products) from an ntensor topology on
spaces of symmetric ntensors products. Indeed, given an ntensor topology on the spaces of symmetric ntensor products we construct an ntensor topology on the spaces of all ntensor products whose restriction to the symmetric ones gives the original topology. Moreover, we prove that when one starts with an ntensor 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 

Additional Information:  Dedicated to the memory of Klaus Floret (19412002) 
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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