相似问题、Folner集与顺从半群的等距表示
Similarity problems, Folner sets and isometric representations of amenable semigroups
摘要：
我们再去一趟Sz Nagy关于希尔伯特空间有界线性算子与等距算子或酉算子相似的判别准则，并给出了新的判别准则.我们还讨论了迪克斯米尔-戴定理关于有界表示的顺从群和半群的同行。我们强调的作用，Folner集在相似性问题中的两个设置的么模，$σ$ -紧凑，顺从的群体和离散半群拥有强Folner条件（SFC）。
英文摘要：
We revisit Sz.-Nagy's criteria for similarity of Hilbert space bounded linear operators to isometries or unitaries and present new ones. We also discuss counterparts of the Dixmier-Day theorem concerning bounded representations of amenable groups and semigroups. We highlight the role of Folner sets in similarity problems in both settings of unimodular, $σ$-compact, amenable groups and in discrete semigroups possessing the Strong Folner condition (SFC).
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