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On Hamel bases in Banach spaces

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Ferrando J.

Studia Mathematica

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2014

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tom 220

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nr 2

169-178

EN

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.

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

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Ferrando J.

Studia Mathematica

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2016

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tom 232

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nr 1

93-94

3

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

100%

Ferrando J.

Studia Mathematica

|

2012

|

tom 210

|

nr 1

93-98

EN

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 $ℓ_{∞}$ if and only if X does.

Ograniczanie wyników

3 Studia Mathematica

3 Ferrando J.

1 2016

1 2014

1 2012

On Hamel bases in Banach spaces

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

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