Displaying similar documents to “Structure of spaces of germs of holomorphic functions.”

Linear topological invariants of spaces of holomorphic functions in infinite dimension.

Nguyen Minh Ha, Le Mau Hai (1995)

Publicacions Matemàtiques

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It is shown that if E is a Frechet space with the strong dual E* then H(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that H(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...

Unsolved Problems

N. Aronszajn, L. Gross, S. Kwapień, N. Nielsen, A. Pełczyński, A. Pietsch, L. Schwartz, P. Saphar, S. Chevet, R. Dudley, D. Garling, N. Kalton, B. Mitjagin, S. Rolewicz, E. Schock, J. Daleckiĭ, J. Dobrakov, B. Gelbaum, G. Henkin, L. Nachbin, N. Peck, L. Waelbroeck, P. Porcelli, M. Rao, M. Zerner, V. Zakharjuta (1970)

Studia Mathematica

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1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

The space of real-analytic functions has no basis

Paweł Domański, Dietmar Vogt (2000)

Studia Mathematica

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Let Ω be an open connected subset of ℝ d . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

On non-primary Fréchet Schwartz spaces

J. Díaz (1997)

Studia Mathematica

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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...