Lifting Commuting 3-Isometric Tuples

Benjamin Russo

An operator $T$ is called a 3-isometry if there exists operators $B_1(T^{\ast },T)$ and $B_2(T^{\ast },T)$ such that \[Q(n)=T^{*n}T^n=1+nB_1(T^*,T)+n^2 B_2(T^*,T)\] for all natural numbers $n$…