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

• Autorzy: José M. Ansemil , Klaus Floret
• Języki publikacji: EN

Abstrakty

EN

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 $E^2$.

Słowa kluczowe

EN

symmetric tensor products; continuous n-homogeneous polynomials; tensor topologies

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy
• 45M05: Asymptotics
• 46A32: Spaces of linear operators; topological tensor products; approximation properties
• 46A03: General theory of locally convex spaces
• 15A69: Multilinear algebra, tensor products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 3
• Strony: 285-295

Daty

wydano

1998

otrzymano

1997-07-02

poprawiono

1997-11-12

Twórcy

autor

José M. Ansemil

• Departamento de Análisis Matemático, Universidad Complutense, 28040 Madrid, Spain.

autor

Klaus Floret

• Fachbereich Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany
• IMECC-Unicamp, C.P. 6065, 13081-970 Campinas, Brasil

Bibliografia

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