Ansemil, José María M. and Floret, Klaus
(1988)
*The symmetric tensor product of a direct sum of locally convex spaces.*
Studia Mathematica, 129
(3).
pp. 285-295.
ISSN 0039-3223

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## Abstract

An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology tau such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for circle times(tau,delta)(n)(F-1 circle plus F-2) gives a direct proof of a recent result of Diaz and Dineen land generalizes it to other topologies tau) that the n-fold projective symmetric and the n-fold projective "full" tensor product of a Iocally convex space fare isomorphic if E is isomorphic to its square E-2.

Item Type: | Article |
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Uncontrolled Keywords: | symmetric tensor products; continuous n-homogeneous polynomials; tensor topologies |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 16794 |

References: | R. Alencar and K. Floret, Weak-strong contínuity of multilinear mappings and the Pelezyński-Pitt-theorem, J. Math. Anal. Appl. 206 (1997), 532-546. A. Arias and J. Farmer, On the structure of tensor products of lp-spaces, Pacific J. Math. 175 (1996), 13-37. F. Blasco, Complementación, casinorrnabilidad y tonelación en espacios de polinomios , doct. thesis, Univ. Compl. Madrid, 1996. F. Blasco, Complementation in spaces of symmetric tensor products and polynomials, Studia Math. 123 (1997) 165-173. J. Bonet and A. Peris, On the injective tensor product of quasinormable spaces, Results in Math. 20 (1991), 431-443. J A. Defan t and K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, North-Holland, 1993. A. Defant and M. Maestre, Property (BB) and holomorphie junetions on Fréchet-Montel spaces, Math. Proc. Cambridge Philos. Soc. 115 (1993), 305-313. J. C. Díaz and S. Dineen, Polynomials on stable spaces, Ark. Mat. to appear. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, in preparation. K. F loret, Some aspeets of the theory locally convex inductive limits, in, Functional Analysis: Surveys and Recent Results II, K, D. Bierstedt and B. Fuchssteiner (ed,.), North-Holland, 1980,205-237. K. F loret, Tensor topologies and equicontinuity, Note Mat. 5 (1985), 37--49. W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach spaces, Bull. London Math. Soc. 28 (1996), 297-304. W. Greub, Multilinear Algebra, Universitext, Springer, 1978. A, Grothendieck, Produits tensoriels et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955. H. Jarchow, Locally Conv ex Spaces, Teubner, 1981. R. Ryan, Applieation of topological tensor products to infinite dimensional holomorphy, doct. thesis, Trinity Coll. Dublin, 1980. L. Schwartz, Théorie des distributions à values vectorielles. I et II, Ann. Inst. Fourier (Grenoble) 7 (1957), 1-141, and 8 (1958), 1-209. |

Deposited On: | 22 Oct 2012 08:57 |

Last Modified: | 07 Feb 2014 09:36 |

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