论文标题
统一的Grothendieck和Kwapień定理多线运算符
Unified Grothendieck's and Kwapień's theorems for multilinear operators
论文作者
论文摘要
Kwapień的定理断言，每个连续的线性操作员从$ \ ell_ {1} $到$ \ ell_ {p} $绝对是$ \ less（r，1 \右）$ -SUMMIMMING，$ 1/r = 1- \ 1- \ weft \ welet \ welet \ welet \ welet \ welet \ vert 1/p-1/p-1/p-1/p-1/p-1/p-1/p-1/p-1/p-1/2 \ right \ vert \ vert。本文研究了这些定理和相关问题的多线性变体。除其他结果外，我们还提供了Kwapień的统一版本和Grothendieck的结果，该版本涵盖了多个求和和绝对求和多线性操作员的情况。
Kwapień's theorem asserts that every continuous linear operator from $\ell_{1}$ to $\ell_{p}$ is absolutely $\left( r,1\right) $-summing for $1/r=1-\left\vert 1/p-1/2\right\vert .$ When $p=2$ it recovers the famous Grothendieck's theorem. In this paper investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapień's and Grothendieck's results that encompasses the cases of multiple summing and absolutely summing multilinear operators.
