Isometric factorization of vector measures and applications to spaces of integrable functions
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2021Metadata
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Dovland, O. & Rodriguez, J. (2021). Isometric factorization of vector measures and applications to spaces of integrable functions. Journal of Mathematical Analysis and Applications, 508(1), 1-16. https://doi.org/10.1016/j.jmaa.2021.125857Abstract
Let X be a Banach space, Σ be a σ-algebra, and be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pełczyński factorization procedure that there exist a reflexive Banach space Y, a vector measure and an injective operator such that m factors as . We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pełczyński factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on is weakly compact, then is equal, up to equivalence of norms, to some where Y is reflexive; here we prove that the above equality can be taken to be isometric.