On exhaustive vector measures.
Quasi totally barrelled spaces
When does bvca (...,X) Contain a Copy of l... ?
Correction to the paper ’Copies of in the space of Pettis integrable functions with integrals of finite variation’ (Studia Math. 210 (2012), 93-98)
Copies of in the space of Pettis integrable functions with integrals of finite variation
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 if and only if X does.
On Hamel bases in Banach spaces
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
Assuming that is a complete probability space and a Banach space, in this paper we investigate the problem of the -inheritance of certain copies of or in the linear space of all [classes of] -valued -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.
On the convergence of certain sums of independent random elements
In this note we investigate the relationship between the convergence of the sequence of sums of independent random elements of the form (where takes the values with the same probability and belongs to a real Banach space for each ) and the existence of certain weakly unconditionally Cauchy subseries of .
A note on copies of in spaces of weak* measurable functions
If is a finite measure space and a Banach space, in this note we show that , the Banach space of all classes of weak* equivalent -valued weak* measurable functions defined on such that a.e. for some equipped with its usual norm, contains a copy of if and only if contains a copy of .
Complemented copies of c in C(Ω).
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 in the bounded linear operator space
In this note we study some properties concerning certain copies of the classic Banach space in the Banach space of all bounded linear operators between a normed space and a Banach space equipped with the norm of the uniform convergence of operators.
Embedding in
If is a measurable space and a Banach space, we provide sufficient conditions on and in order to guarantee that , the Banach space of all -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of if and only if does.
A revised closed graph theorem for quasi-Suslin spaces
Some results about the continuity of special linear maps between -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 is said to have a (relatively countably) compact...
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