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Absolutely ( q , 1)-summing operators acting in C ( K )-spaces and the weighted Orlicz property for Banach spaces
Positivity ( IF 0.8 ) Pub Date : 2021-01-19 , DOI: 10.1007/s11117-021-00811-y
J. M. Calabuig , E. A. Sánchez Pérez

We provide a new separation-based proof of the domination theorem for (q, 1)-summing operators. This result gives the celebrated factorization theorem of Pisier for (q, 1)-summing operators acting in C(K)-spaces. As far as we know, none of the known versions of the proof uses the separation argument presented here, which is essentially the same that proves Pietsch Domination Theorem for p-summing operators. Based on this proof, we propose an equivalent formulation of the main summability properties for operators, which allows to consider a broad class of summability properties in Banach spaces. As a consequence, we are able to show new versions of the Dvoretzky–Rogers Theorem involving other notions of summability, and analyze some weighted extensions of the q-Orlicz property.



中文翻译:

在C(K)空间中起作用的绝对(q,1)个算子和Banach空间的加权Orlicz属性

我们为(q,1)加和运算符提供了一个新的基于分离的控制定理的证明。这个结果给出了在(CK)空间中作用的(q,1)个求和算子的Pisier著名的因式分解定理。据我们所知,证明的已知版本均未使用此处提出的分离参数,该参数与证明p的Pietsch支配定理基本相同求和运算符。基于此证明,我们为算子提出了主要可加性的等价表示形式,它允许考虑Banach空间中一类广泛的可加性。结果,我们能够展示涉及其他可加性概念的Dvoretzky-Rogers定理的新版本,并分析q -Orlicz属性的一些加权扩展。

更新日期:2021-01-19
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