Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let X be a Banach space and ν a countably additive X-valued measure defined on a σ-algebra. We discuss some generation properties of the Banach space L¹(ν) and its connection with uniform Eberlein compacta. In this way, we provide a new proof that L¹(ν) is weakly compactly generated and embeds isomorphically into a Hilbert generated Banach space. The Davis-Figiel-Johnson-Pełczyński factorization of the integration operator $I_{ν}: L¹(ν) → X$ is also analyzed. As a result, we prove that if $I_{ν}$ is both completely continuous and Asplund, then ν has finite variation and L¹(ν) = L¹(|ν|) with equivalent norms.
Słowa kluczowe
Kategorie tematyczne
- 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
- 47B07: Operators defined by compactness properties
- 46B50: Compactness in Banach (or normed) spaces
- 46G10: Vector-valued measures and integration
Czasopismo
Rocznik
Tom
Numer
Strony
115-125
Opis fizyczny
Daty
wydano
2016
Twórcy
autor
- Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo (Murcia), Spain
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm6735-11-2015