Resolution of identity in certain metrizable locally convex spaces.

M. Valdivia

Displaying similar documents to “Resolution of identity in certain metrizable locally convex spaces.”

The space $D (U)$ is not $B_{r}$ -complete

Manuel Valdivia (1977)

Annales de l'institut Fourier

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Certain classes of locally convex space having non complete separated quotients are studied and consequently results about $B_{r}$ -completeness are obtained. In particular the space of L. Schwartz $D (Ω)$ is not $B_{r}$ -complete where $Ω$ denotes a non-empty open set of the euclidean space $R^{m}$ .

Eberlein compacts in $L_{1} (X)$

Jürgen Batt, Georg Schlüchtermann (1986)

Studia Mathematica

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On the structure of certain ultradistributions.

M. Valdivia (2009)

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The space of countably simple bounded functions with values in a DF-space.

S. Díaz, A. Fernández, M. Florencio, P. J. Paúl (1994)

Revista Matemática de la Universidad Complutense de Madrid

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Representing and absolutely representing systems

V. Kadets, Yu. Korobeĭnik (1992)

Studia Mathematica

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We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.

The approximation property of order p in locally convex spaces.

J. A. López Molina (1986)

Collectanea Mathematica

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Barreledness of subspaces of countable codimension and the closed graph theorem

D. Van Dulst (1972)

Compositio Mathematica

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Mean ergodic theorem in locally convex linear topological spaces

M. Altman (1953)

Studia Mathematica

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On $B_{r}$ -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

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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.