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

José Ansemil; Klaus Floret

Studia Mathematica (1998)

  • Volume: 129, Issue: 3, page 285-295
  • ISSN: 0039-3223

Abstract

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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 .

How to cite

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Ansemil, José, and Floret, Klaus. "The symmetric tensor product of a direct sum of locally convex spaces." Studia Mathematica 129.3 (1998): 285-295. <http://eudml.org/doc/216505>.

@article{Ansemil1998,
abstract = {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 $⨂^n_\{τ,s\} (F_1⨁ F_2)$ 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 $E^2$.},
author = {Ansemil, José, Floret, Klaus},
journal = {Studia Mathematica},
keywords = {symmetric tensor products; continuous n-homogeneous polynomials; tensor topologies; full tensor product; polynomials on Banach spaces},
language = {eng},
number = {3},
pages = {285-295},
title = {The symmetric tensor product of a direct sum of locally convex spaces},
url = {http://eudml.org/doc/216505},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Ansemil, José
AU - Floret, Klaus
TI - The symmetric tensor product of a direct sum of locally convex spaces
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 3
SP - 285
EP - 295
AB - 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 $⨂^n_{τ,s} (F_1⨁ F_2)$ 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 $E^2$.
LA - eng
KW - symmetric tensor products; continuous n-homogeneous polynomials; tensor topologies; full tensor product; polynomials on Banach spaces
UR - http://eudml.org/doc/216505
ER -

References

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