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

Improving integrability via absolute summability: a general version of Diestel’s Theorem 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 $$(p,\sigma )$$ ( 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), $$L^p$$ L p and Hilbert spaces—and operators—p-summing, (q, p)-summing and p-approximable operators. Positivity Springer Journals

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

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Springer International Publishing
Copyright © 2015 by Springer Basel
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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