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

José AnsemilKlaus Floret — 1998

Studia Mathematica

An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for τ , s n ( F 1 F 2 ) gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square E 2 .

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