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• # Artykuł - szczegóły

## Colloquium Mathematicum

2016 | 144 | 1 | 115-125

## Factorization of vector measures and their integration operators

EN

### Abstrakty

EN
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.

115-125

wydano
2016

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