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When does bvca (...,X) Contain a Copy of l... ?

Juan Carlos Ferrando — 1994

Mathematica Scandinavica

Correction to the paper ’Copies of $ℓ_{\infty}$ in the space of Pettis integrable functions with integrals of finite variation’ (Studia Math. 210 (2012), 93-98)

Juan Carlos Ferrando — 2016

Studia Mathematica

Copies of $ℓ_{\infty}$ in the space of Pettis integrable functions with integrals of finite variation

Juan Carlos Ferrando — 2012

Studia Mathematica

Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. We show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of $ℓ_{\infty}$ if and only if X does.

On Hamel bases in Banach spaces

Juan Carlos Ferrando — 2014

Studia Mathematica

It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.

On Pettis integrability

Juan Carlos Ferrando — 2003

Czechoslovak Mathematical Journal

Assuming that $(Ω, Σ, μ)$ is a complete probability space and $X$ a Banach space, in this paper we investigate the problem of the $X$ -inheritance of certain copies of $c_{0}$ or $ℓ_{\infty}$ in the linear space of all [classes of] $X$ -valued $μ$ -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.

On the convergence of certain sums of independent random elements

Juan Carlos Ferrando — 2002

Commentationes Mathematicae Universitatis Carolinae

In this note we investigate the relationship between the convergence of the sequence ${S_{n}}$ of sums of independent random elements of the form $S_{n} = \sum_{i = 1}^{n} ε_{i} x_{i}$ (where $ε_{i}$ takes the values $\pm 1$ with the same probability and $x_{i}$ belongs to a real Banach space $X$ for each $i \in ℕ$ ) and the existence of certain weakly unconditionally Cauchy subseries of $\sum_{n = 1}^{\infty} x_{n}$ .

A note on copies of $c_{0}$ in spaces of weak* measurable functions

Juan Carlos Ferrando — 2000

Commentationes Mathematicae Universitatis Carolinae

If $(Ω, Σ, μ)$ is a finite measure space and $X$ a Banach space, in this note we show that $L_{w^{*}}^{1} (μ, X^{*})$ , the Banach space of all classes of weak* equivalent $X^{*}$ -valued weak* measurable functions $f$ defined on $Ω$ such that $∥ f (ω) ∥ \leq g (ω)$ a.e. for some $g \in L_{1} (μ)$ equipped with its usual norm, contains a copy of $c_{0}$ if and only if $X^{*}$ contains a copy of $c_{0}$ .

Complemented copies of c in C(Ω).

Juan Carlos Ferrando; Manuel López Pellicer — 2001

RACSAM

En esta nota consideramos una clase de espacios topológicos de Hausdorff localmente compactos (Ω) con la propiedad de que el espacio de Banach C(Ω) de todas las funciones continuas con valores escalares definidas en Ω que se anulan en el infinito, equipado con la norma supremo, contiene una copia de C norma-uno complementada, mientras que C (βΩ) contiene una copia de l linealmente isométrica.

On copies of $c_{0}$ in the bounded linear operator space

Juan Carlos Ferrando; J. M. Amigó — 2000

Czechoslovak Mathematical Journal

In this note we study some properties concerning certain copies of the classic Banach space $c_{0}$ in the Banach space $ℒ (X, Y)$ of all bounded linear operators between a normed space $X$ and a Banach space $Y$ equipped with the norm of the uniform convergence of operators.

Embedding $c_{0}$ in $bvca (Σ, X)$

Juan Carlos Ferrando; L. M. Sánchez Ruiz — 2007

Czechoslovak Mathematical Journal

If $(Ω, Σ)$ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $Σ$ and $X$ in order to guarantee that $b v c a (Σ, X)$ , the Banach space of all $X$ -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_{0}$ if and only if $X$ does.

A revised closed graph theorem for quasi-Suslin spaces

Juan Carlos Ferrando; J. Kąkol; M. Lopez Pellicer — 2009

Czechoslovak Mathematical Journal

Some results about the continuity of special linear maps between $F$ -spaces recently obtained by Drewnowski have motivated us to revise a closed graph theorem for quasi-Suslin spaces due to Valdivia. We extend Valdivia’s theorem by showing that a linear map with closed graph from a Baire tvs into a tvs admitting a relatively countably compact resolution is continuous. This also applies to extend a result of De Wilde and Sunyach. A topological space $X$ is said to have a (relatively countably) compact...