关于Haar酉元的一个注记

A note on Haar unitary element

设M是一个II1型因子,τ是M的正规的、忠实的迹态,U∈M是一个Haar酉元,p∈M是一个投影,τ(p)=n1(n3,n∈Z),p和U自由.我们用初等方法证明了若pUp=wh是pUp的极分解,则w也是一个Haar酉元且w和h是自由的.我们还给出了pUp的矩的刻画.

Suppose M be a factor of type II1 with a normal faithful tracial state τ,U ∈ M is a Haar unitary,p ∈ M is a projection with τ（p） = n1（n 3,n ∈ Z）,p and U are free.We give an elementary proof of the fact that if pUp = wh is the polar decomposition of pUp,then w is also a Haar unitary element and w and h are free.A characterization of the moments of pUp is also given.