一个Kwapiesten定理的非线性变式
Nonlinear variants of a theorem of Kwapień
摘要：
S. Kwapiestan断言从巴拿赫空间到希尔伯特空间的线性算子绝对是$1$ -求和的，只要它的伴随绝对是$q$ -求和的，对于某些$1\leq q<\infty$ ;这个结果最近被Chen和Zheng推广到Lipschitz算子。在本文中，我们表明，Kwapiestan的和陈-郑定理举行在一个非常宽松的非线性环境下，较弱的假设。即使限制到原来的线性情况下，我们的结果推广了Kwapieste定理，因为它持有时，伴随只是几乎求和。此外，提供了$\mathcal{L}_{p}$ -空间的变体，其中$p\geq2$代替希尔伯特空间。
英文摘要：
A famous result of S. Kwapień asserts that a linear operator from a Banach space to a Hilbert space is absolutely $1$-summing whenever its adjoint is absolutely $q$-summing for some $1\leq q<\infty$; this result was recently extended to Lipschitz operators by Chen and Zheng. In the present paper we show that Kwapień's and Chen--Zheng theorems hold in a very relaxed nonlinear environment, under weaker hypotheses. Even when restricted to the original linear case, our result generalizes Kwapień's theorem because it holds when the adjoint is just almost summing. In addition, a variant for $\mathcal{L}_{p}$-spaces, with $p\geq2$, instead of Hilbert spaces is provided.
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。
