论文标题
calkin运算符上的对称功能的PIETSCH对应关系，与半蛋白石von Neumann代数相关
Pietsch correspondence for symmetric functionals on Calkin operator spaces associated with semifinite von Neumann algebras
论文作者
论文摘要
在本文中，我们将紧凑型运算符和痕迹理想的Pietsch对应关系扩展到半决赛设置。我们证明，由$ \ z $索引的序列的移位 - 单声道空间$ e（\ z）$定义了$τ$的calkin space $ e（\ cm，τ）$ - 可容纳的运算符，隶属于属于von neumann algebra $ \ cm \ cm \ cm \ cm \ cm \ cm \ cm \ cm \ cm fluths fauith forage fluith此外，我们表明$ e（\ z）$上的Shift-Invariant函数在$ e（\ cm，τ）$上生成对称函数。在特殊情况下，当代数$ \ cm $是原子或原子相等的原子时，相反的也会成立，我们在所有移位 - 马诺酮空间$ e（\ z）$ e（\ z）$和calkin spaces $ e（\ cm，τ）$和sermentive n of thehiant-Invariant $ e（e zextive z）$ z的$ e（\ cm cm e（\ z）$ e（\ z）$ e（\ z）$（\ z）$ e（\ z）$ e（\ z）$ e（＆e z）之间的caliptials $ e（e（calkin $ e（\ cm，τ）$。 Bijective对应关系$ e（\ Z）\ leftrightArrows E（\ cm，τ）$扩展到完全对称$δ$ normed spaces $ e（\ cm，τ）$和完整$Δ$Δ$ normed shift-normed shift-shift-shift-monotone Space $ e（\ z）$之间的对应关系。
In this paper we extend the Pietsch correspondence for ideals of compact operators and traces on them to the semifinite setting. We prove that a shift-monotone space $E(\Z)$ of sequences indexed by $\Z$ defines a Calkin space $E(\cM,τ)$ of $τ$-measurable operators affiliated with a semifinite von Neumann algebra $\cM$ equipped with a faithful normal semifinite trace $τ$. Furthermore, we show that shift-invariant functionals on $E(\Z)$ generate symmetric functionals on $E(\cM,τ)$. In the special case, when the algebra $\cM$ is atomless or atomic with atoms of equal trace, the converse also holds and we have a bijective correspondence between all shift-monotone spaces $E(\Z)$ and Calkin spaces $E(\cM,τ)$ as well as a bijective correspondence between shift-invariant functionals on $E(\Z)$ and symmetric functionals on $E(\cM,τ)$. The bijective correspondence $E(\Z)\leftrightarrows E(\cM,τ)$ extends to a correspondence between complete symmetrically $Δ$-normed spaces $E(\cM,τ)$ and complete $Δ$-normed shift-monotone spaces $E(\Z)$.
