Complementation in spaces of symmetric tensor products and polynomials

• Autorzy: Fernando Blasco
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

symmetric tensor; polynomial; complementation

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy
• 46A03: General theory of locally convex spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 123
• Numer: 2
• Strony: 165-173

Daty

wydano

1997

otrzymano

1996-07-09

poprawiono

1996-09-28

Twórcy

autor

Fernando Blasco

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

Bibliografia

• [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 $τ_0$ and $τ_ω$ 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.