Geodesic
The symmetric tensor product of a direct sum of locally convex spaces
Studia Mathematica, Tome 129 (1998) no. 3, pp. 285-295

Voir la notice de l'article provenant de 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 $E^2$.
DOI : 10.4064/sm-129-3-285-295
Keywords: symmetric tensor products, continuous n-homogeneous polynomials, tensor topologies

José M Ansemil 1 ;  1

1 
@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},
     publisher = {mathdoc},
     volume = {129},
     number = {3},
     year = {1998},
     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
PB  - mathdoc
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  - 
%0 Journal Article
%A José M  Ansemil
%A  
%T The symmetric tensor product of a direct sum of locally convex spaces
%J Studia Mathematica
%D 1998
%P 285-295
%V 129
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-129-3-285-295/
%R 10.4064/sm-129-3-285-295
%G en
%F 10_4064_sm_129_3_285_295
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

Cité par Sources :