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1997 | 126 | 3 | 291-307
Tytuł artykułu

On non-primary Fréchet Schwartz spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions of bounded type $ℋ_b(U)$, where U is a Banach space or a bounded absolutely convex open set in a Banach space.
Twórcy
autor
  • Departamento de Matemáticas, E.T.S.I.A.M., Universidad de Córdoba, 14004 Córdoba, Spain, ma1dialj@uco.es
Bibliografia
  • [1] A. Albanese, Primary products of Banach spaces, Arch. Math. (Basel) 66 (1996), 397-405.
  • [2] A. Albanese, Montel subspaces in Fréchet spaces of Moscatelli type, Glasgow Math. J., to appear.
  • [3] A. Albanese and V. B. Moscatelli, The spaces $(ℓ_p)^ℕ ∩ ℓ_q(ℓ_q)$, 1 ≤ p < q ≤ ∞ are primary, preprint.
  • [4] A. Albanese and V. B. Moscatelli, Complemented subspaces of sums and products of copies of $L^1[0,1]$, Rev. Mat. Univ. Complut. Madrid 9 (1996), 275-287.
  • [5] A. Benndorf, On the relation of the bounded approximation property and a finite dimensional decomposition in nuclear Fréchet spaces, Studia Math. 75 (1983), 103-119.
  • [6] C. Bessaga, Geometrical methods of the theory of Fréchet spaces, in: Functional Analysis and its Applications, H. Hogbe-Nlend (ed.), World Sci., Singapore, 1988, 1-34.
  • [7] K. D. Bierstedt, R. G. Meise and N. H. Summers, Köthe sets and Köthe sequence spaces, in: Functional Analysis, Holomorphy and Approximation Theory, North-Holland Math. Stud. 71, North-Holland, Amsterdam, 1982, 27-91.
  • [8] J. Bonet and J. C. Díaz, On the weak quasinormability condition of Grothendieck, Tr. J. Math. 15 (1991), 154-164.
  • [9] J. Bonet and S. Dierolf, Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (1989), 77-92.
  • [10] J. M. F. Castillo, J. C. Díaz and J. Motos, On the Fréchet space $L_p^-$, preprint.
  • [11] J. C. Díaz, Primariness of some universal Fréchet spaces, in: Functional Analysis, S. Dierolf, S. Dineen and P. Domański (eds.), de Gruyter, Berlin, 1996, 95-103.
  • [12] J. C. Díaz and M. A. Miñarro, Universal Köthe sequence spaces, Monatsh. Math., to appear.
  • [13] J. C. Díaz and S. Dineen, Polynomials on stable spaces, Ark. Mat., to appear.
  • [14] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, Amsterdam, 1981.
  • [15] S. Dineen, Quasinormable spaces of holomorphic functions, Note Mat. 13 (1993), 155-195.
  • [16] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, Isomorphic classification of cartesian products of power series spaces, Michigan Math. J. 43 (1996), 221-229.
  • [17] P. B. Djakov and V. P. Zahariuta, On Dragilev type power Köthe spaces, Studia Math. 120 (1996), 219-234.
  • [18] P. Domański and A. Ortyński, Complemented subspaces of products of Banach spaces, Trans. Amer. Math. Soc. 316 (1989), 215-231.
  • [19] P. Galindo, M. Maestre and P. Rueda, Biduality in spaces of holomorphic functions, preprint.
  • [20] J. M. Isidro, Quasinormability of some spaces of holomorphic mappings, Rev. Mat. Univ. Complut. Madrid 3 (1990), 13-17.
  • [21] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981.
  • [22] G. Köthe, Topological Vector Spaces, I, Springer, New York, 1969.
  • [23] G. Metafune and V. B. Moscatelli, Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. 153 (1988), 175-190.
  • [24] G. Metafune and V. B. Moscatelli, On the space $ℓ_{p^+}=∩_{q>p}ℓ_q$, Math. Nachr. 147 (1990), 47-52.
  • [25] A. Peris, Quasinormable spaces and the problem of topologies of Grothendieck, Ann. Acad. Sci. Fenn. Ser. A I Math. 19 (1994), 167-203.
  • [26] T. Terzioğlu and D. Vogt, A Köthe space which has a continuous norm but whose bidual does not, Arch. Math. (Basel) 54 (1990), 180-183.
  • [27] V. P. Zahariuta, Linear topological invariants and their applications to isomorphic classification of generalized power spaces, Rostov. Univ., 1979 (in Russian); revised English version: Turkish J. Math. 20 (1996), 237-289.
Typ dokumentu
Bibliografia
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