Download PDF - Complementation in spaces of symmetric tensor products and polynomialsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Complementation in spaces of symmetric tensor products and polynomials

Authors 1

Affiliations

  1. Unidad Docente de Matemáticas, E.T.S.I. de Montes, Universidad Politécnica de Madrid, 28040 Madrid, Spain

Abstract

For a locally convex space E we prove that the space of n-symmetric tensors is complemented in the space of (n+1)-symmetric tensors endowed with the projective topology. Applications and related results are also given.

Keywords

ENG
symmetric tensor, polynomial, complementation

Bibliography

  1. J. M. Ansemil and S. Ponte, The compact open and the Nachbin ported topologies on spaces of holomorphic functions, Arch. Math. (Basel) 51 (1988), 65-70.
  2. J. M. Ansemil and J. Taskinen, On a problem of topologies in infinite dimensional holomorphy, ibid. 54 (1990), 61-64.
  3. R. M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Anal. 21 (1976), 7-30.
  4. A. Defant and M. Maestre, Property (BB) and holomorphic functions on Fréchet-Montel spaces, Math. Proc. Cambridge Philos. Soc. 115 (1993), 305-313.
  5. S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, New York, 1981.
  6. S. Dineen, Holomorphic functions on Fréchet-Montel spaces, J. Math. Anal. Appl. 163 (1992), 581-587.
  7. S. Dineen, Holomorphic functions and the (BB)-property, Math. Scand. 74 (1994), 215-236.
  8. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, to appear.
  9. P. Galindo, D. García and M. Maestre, The coincidence of τ0 and τω for spaces of holomorphic functions on some Fréchet-Montel spaces, Proc. Roy. Irish Acad. Sect. A 91 (1991), 137-143.
  10. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  11. H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981.
  12. G. Köthe, Topological Vector Spaces I, Grundlehren Math. Wiss. 159, 2nd ed., Springer, New York, 1969.
  13. G. Köthe, Topological Vector Spaces II, Grundlehren Math. Wiss. 237, Springer, New York, 1979.
  14. R. A. Ryan, Applications of topological tensor products to infinite dimensional holomorphy, Ph.D. Thesis Trinity College, Dublin, 1980.
  15. J. Taskinen, Counterexamples to "Problème des topologies" of Grothendieck, Ann. Acad. Sci. Fenn. Ser. A I Math. 63 (1986), 1-25.
Studia Mathematica
1997/123/2
Export to PBN, Opens in new tab
Pages:
165-173
Main language of publication
English
Received
1996-07-09
Accepted
1996-09-28
Published
1997
Exact and natural sciences