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

Studia Mathematica (1998)

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

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topAnsemil, 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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- [11] K. Floret, Tensor topologies and equicontinuity, Note Mat. 5 (1985), 37-49. Zbl0654.46061
- [12] W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach spaces, Bull. London Math. Soc. 28 (1996), 297-304. Zbl0863.46006
- [13] W. Greub, Multilinear Algebra, Universitext, Springer, 1978.
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- [15] H. Jarchow, Locally Convex Spaces, Teubner, 1981. Zbl0466.46001
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