用绝对可和性改进可积性：Diestel定理的一个推广
Improving integrability via absolute summability: a general version of Diestel's Theorem
摘要：
一个经典的结果由J. Diestel建立，一个求和算子与一个（强可测的）Pettis可积函数的复合给出了一个Bochner可积函数。在本文中，我们证明了一个更一般的结果是可能的，关于改善可积性的向量值函数的运营商。在证明了一般结果之后，我们将注意力集中在$(p,σ)$ -绝对连续算子给出的特殊情况下，这使得我们可以证明许多关于经典巴拿赫空间--包括$C(K)$，$L^p$和希尔伯特空间--和算子-- $p$ -求和，$(q,p)$ -求和和$p$ -可逼近算子--的特定情况下的积分改进的特殊结果。
英文摘要：
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---.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
