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arXiv · 1502.01970

Improving integrability via absolute summability: a general version of Diestel's Theorem

Daniel Pellegrino·Pilar Rueda·Enrique Sánchez-Pérez
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Abstract

A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis integrable function gives a Bochner integrable function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the $(p,σ)$-absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces ---including $C(K)$, $L^p$ and Hilbert spaces--- and operators ---$p$-summing, $(q,p)$-summing and $p$-approximable operators---.

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Daniel Pellegrino, Pilar Rueda, Enrique Sánchez-Pérez. 2015-02-06. Improving integrability via absolute summability: a general version of Diestel's Theorem. https://doi.org/10.1007/s11117-015-0361-5

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