The symmetric tensor product of a direct sum of locally convex spaces
Studia Mathematica, Tome 129 (1998) no. 3, pp. 285-295
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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 $E^2$.
Keywords:
symmetric tensor products, continuous n-homogeneous polynomials, tensor topologies
@article{10_4064_sm_129_3_285_295,
author = {Jos\'e M Ansemil and },
title = {The symmetric tensor product of a direct sum of locally convex spaces},
journal = {Studia Mathematica},
pages = {285--295},
year = {1998},
volume = {129},
number = {3},
doi = {10.4064/sm-129-3-285-295},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-129-3-285-295/}
}
TY - JOUR AU - José M Ansemil AU - TI - The symmetric tensor product of a direct sum of locally convex spaces JO - Studia Mathematica PY - 1998 SP - 285 EP - 295 VL - 129 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-129-3-285-295/ DO - 10.4064/sm-129-3-285-295 LA - en ID - 10_4064_sm_129_3_285_295 ER -
José M Ansemil; . The symmetric tensor product of a direct sum of locally convex spaces. Studia Mathematica, Tome 129 (1998) no. 3, pp. 285-295. doi: 10.4064/sm-129-3-285-295
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