论文标题
Kwapień定理的非线性变体
Nonlinear variants of a theorem of Kwapień
论文作者
论文摘要
S.Kwapień的著名结果断言，从Banach空间到Hilbert Space的线性操作员绝对是$ 1 $ - 每当它的伴随绝对是$ Q $ -SMUMM，以$ 1 \ leq q <\ iffty $；最近，该结果扩展到了Chen和Zheng的Lipschitz运营商。在本文中，我们表明Kwapień和Chen-Zheng定理在较弱的假设下，在非常放松的非线性环境中持有。即使仅限于原始线性案例，我们的结果也概括了Kwapień定理，因为当伴随几乎求和时，它成立。此外，提供了$ \ mathcal {l} _ {p} $的变体，带有$ p \ geq2 $，而不是希尔伯特空格。
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.
