Factorization of vector measures and their integration operators

• Autorzy: José Rodríguez
• Języki publikacji: 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.

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 1
• Strony: 115-125

Daty

wydano

2016

Twórcy

autor

José Rodríguez

• Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo (Murcia), Spain

Identyfikatory

DOI

10.4064/cm6735-11-2015