Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on ${\mathcal {H}} (U) $

Sean Dineen

Displaying similar documents to “Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$ ”

A lifting theorem for locally convex subspaces of $L_{0}$

R. Faber (1995)

Studia Mathematica

Similarity:

We prove that for every closed locally convex subspace E of $L_{0}$ and for any continuous linear operator T from $L_{0}$ to $L_{0} / E$ there is a continuous linear operator S from $L_{0}$ to $L_{0}$ such that T = QS where Q is the quotient map from $L_{0}$ to $L_{0} / E$ .

Holomorphy types on a Banach spaces

Seán Dineen (1971)

Studia Mathematica

Similarity:

Quasinormability of some spaces of holomorphic mappings.

José M. Isidro (1990)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.

On $B_{r}$ -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

Similarity:

In this paper it is proved that if ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are two sequences of infinite-dimensional Banach spaces then $H = (\oplus_{n = 1}^{\infty} E_{n}) \times \prod_{n = 1}^{\infty} F_{n}$ is not $B_{r}$ -complete. If ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are also reflexive spaces there is on $H$ a separated locally convex topology $ℱ$ , coarser than the initial one, such that $H [ℱ]$ is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on $B_{r}$ -completeness and bornological spaces.

Symmetric bases of locally convex spaces

D. Garling (1968)

Studia Mathematica

Similarity:

Some characterizations of ultrabornological spaces

Manuel Valdivia (1974)

Annales de l'institut Fourier

Similarity:

Let $U$ be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let $F$ be an infinite-dimensional Banach space. Then $F$ is the inductive limit of a family of spaces equal to $E$ . The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let $Ω$ be a non-empty open set in the euclidean $n$ -dimensional space $R^{n}$ . Then $F$ is the inductive limit of a family of spaces equal to $D (Ω)$ . ...

On the complemented subspaces of the Schreier spaces

I. Gasparis, D. Leung (2000)

Studia Mathematica

Similarity:

It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space $X^{ξ}$ generated by subsequences $(e_{l_{n}}^{ξ})$ and $(e_{m_{n}}^{ξ})$ , respectively, of the natural Schauder basis $(e_{n}^{ξ})$ of $X^{ξ}$ are isomorphic if and only if $(e_{l_{n}}^{ξ})$ and $(e_{m_{n}}^{ξ})$ are equivalent. Further, $X^{ξ}$ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of $(e_{n}^{ξ})$ . It is also shown that there exists a complemented subspace spanned by a block basis of $(e_{n}^{ξ})$ , which is not isomorphic to a subspace generated by a subsequence of $(e_{n}^{ζ})$ ,...

Integration of evolution equations in a locally convex space

V. Babalola (1974)

Studia Mathematica

Similarity:

Displaying similar documents to “Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on ℋ ( U ) ”

Displaying similar documents to “Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$ ”