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The symmetric tensor product of a direct sum of locally convex spaces

Ansemil, José María M. and Floret, Klaus (1988) The symmetric tensor product of a direct sum of locally convex spaces. Studia Mathematica, 129 (3). pp. 285-295. ISSN 0039-3223

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Abstract

An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology tau such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for circle times(tau,delta)(n)(F-1 circle plus F-2) gives a direct proof of a recent result of Diaz and Dineen land generalizes it to other topologies tau) that the n-fold projective symmetric and the n-fold projective "full" tensor product of a Iocally convex space fare isomorphic if E is isomorphic to its square E-2.

Item Type:Article
Uncontrolled Keywords:symmetric tensor products; continuous n-homogeneous polynomials; tensor topologies
Subjects:Sciences > Mathematics > Topology
ID Code:16794
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