内插求和算子理想的包含结果与向量值函数可积性的改进
Some inclusion results for interpolated summing operator ideals and integrability improvement of vector valued functions
摘要：
考虑一个巴拿赫空间值可测函数$f$和一个来自{ $f$ }取值空间的算子$u$。如果$f $是Pettis可积的，则J. Diestel的一个经典结果表明，只要$u$是绝对求和的，将其与$u$组合就得到Bochner可积函数$u \circ f$。在以前的工作中，我们已经表明，一个众所周知的插值技术算子理想允许证明在某些要求下，一个组成的$p$ -佩蒂斯可积函数与$q$ -求和算子提供了一个$r$ -Bochner可积函数。本文证明了{抽象}和算子类的一个新的抽象包含定理，并将其应用于插值算子理想类。与前面的结果一起，提供了关于函数$u \circ f$的可积性与函数$u$的可和性之间关系的更多结果.
英文摘要：
Consider a Banach space valued measurable function $f$ and an operator $u$ from the space where {$f$} takes values. If $f $ is Pettis integrable, a classical result due to J. Diestel shows that composing it with $u$ gives a Bochner integrable function $u \circ f$ whenever $u$ is absolutely summing. In a previous work we have shown that a well-known interpolation technique for operator ideals allows to prove under some requirements that a composition of a $p$-Pettis integrable function with a $q$-summing operator provides an $r$-Bochner integrable function. In this paper a new abstract inclusion theorem for classes of {abstract} summing operators is shown and applied to the class of interpolated operator ideals. Together with the results of the {aforementioned} paper, it provides more results on the relation about the integrability of the function $u \circ f$ and the summability properties of $u$.
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