EuDML | Browse

It is proved that every real metrizable locally convex space which is not nuclear contains a closed additive subgroup K such that the quotient group G = (span K)/K admits a non-trivial continuous positive definite function, but no non-trivial continuous character. Consequently, G cannot satisfy any form of the Bochner theorem.

Quotient spaces of (s) with basis

Ed Dubinsky, William Robinson (1978)

Studia Mathematica

Real Analytic Curves in Fréchet Spaces and Their Duals.

José Bonet, Pawel Domanski (1998)

Monatshefte für Mathematik

Rearrangement of series in nonnuclear spaces

Wojciech Banaszczyk (1993)

Studia Mathematica

It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.

Regular methods of summability in some locally convex spaces

Costas Poulios (2009)

Commentationes Mathematicae Universitatis Carolinae

Suppose that $X$ is a Fréchet space, $〈 a_{i j} 〉$ is a regular method of summability and $(x_{i})$ is a bounded sequence in $X$ . We prove that there exists a subsequence $(y_{i})$ of $(x_{i})$ such that: either (a) all the subsequences of $(y_{i})$ are summable to a common limit with respect to $〈 a_{i j} 〉$ ; or (b) no subsequence of $(y_{i})$ is summable with respect to $〈 a_{i j} 〉$ . This result generalizes the Erdös-Magidor theorem which refers to summability of bounded sequences in Banach spaces. We also show that two analogous results for some $ω_{1}$ -locally convex spaces...

Remarks on bases in a Fréchet function space.

Päivi Mattila, Jari Taskinen (1993)

Revista Matemática de la Universidad Complutense de Madrid

Remarks on independent sequences and dimension in topological linear spaces.

Z. Lipecki (1998)

Collectanea Mathematica

Remarks on the existence of unconditional bases for weighted countably-Hilbert spaces and their complemented subspaces.

Kondakov, V.P. (2001)

Sibirskij Matematicheskij Zhurnal

Représentation fonctionnelle des espaces vectoriels toplogiques

Philippe Turpin (1982)

Studia Mathematica

Representation of continuous linear functionals on a subspace of a countable Cartesien product of Banach spaces

A. Jakimowski, D. Russell (1982)

Studia Mathematica

Representations of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$

A. Albanese, V. Moscatelli (2000)

Studia Mathematica

We give a representation of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^{\infty} (ℝ^{N}) \cap H^{k, 2} (ℝ^{N})$ is isomorphic to the sequence space $s^{ℕ} \cap l^{2} (l^{2})$ , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

Currently displaying 181 – 200 of 271

Previous Page 10 Next

Displaying 181 – 200 of 271

Pseudo-completeness in linear metrizable spaces

Quasi-bounded sets.

Quasi-complements in F-spaces

Quasinormable spaces and the problem of topologies of Grothendieck.

Quasinormable spaces of polynomials.

Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely

Quotient spaces of (s) with basis

Real Analytic Curves in Fréchet Spaces and Their Duals.

Rearrangement of series in nonnuclear spaces

Regular methods of summability in some locally convex spaces

Remarks on bases in a Fréchet function space.

Remarks on independent sequences and dimension in topological linear spaces.

Remarks on the existence of unconditional bases for weighted countably-Hilbert spaces and their complemented subspaces.

Représentation fonctionnelle des espaces vectoriels toplogiques

Representation of continuous linear functionals on a subspace of a countable Cartesien product of Banach spaces

Representations of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$

Resolution of identity in certain metrizable locally convex spaces.

R-Schauder decompositions. Some applications.

Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.

Sequence space representations for (FN)-algebras of entire functions modulo closed ideals

Currently displaying 181 – 200 of 271