论文标题
关于G. Pisier和P. Saab关于卷积的一些结果的评论
Remarks on some results of G. Pisier and P. Saab on convolutions
论文作者
论文摘要
G. Pisier的结果说，卷积操作员$ \ star f：m（g）\ to c（g），$ g $是一个紧凑的阿贝尔人集团，只有$ f $具有绝对可总结的一组傅立叶系数，才能通过希尔伯特空间来考虑。萨博（P.我们进一步概括了G. pisier和P. Saab的结果，特别是考虑到操作员通过希尔伯特空间中的Schatten类的操作员的因素化。此外，还获得了一些有关操作员通过Lorentz-Schatten类的操作员分解的相关定理。
A result of G. Pisier says that a convolution operator $\star f : M(G) \to C(G),$ where $G$ is a compact Abelian group, can be factored through a Hilbert space if and only if $f$ has the absolutely summable set of Fourier coefficients. P. Saab (2010) generalized this result in some directions in the vector-valued cases. We give some further generalizations of the results of G. Pisier and P. Saab, considering, in particular, the factorizations of the operators through the operators of Schatten classes in Hilbert spaces. Also, some related theorem on the factorization of operators through the operators of the Lorentz-Schatten classes are obtained.
