INVERTIBLE WEIGHTED SHIFT OPERATORS WHICH ARE m-ISOMETRIES.

For a bounded linear operator T on a complex Hilbert space H, let ΔT,m = Σ m k=0(-1)k ( m k ) T"m-kTm-k for m ∊ N. T is called an misometry if ΔT,m = 0. In this paper, for every even number m, we give an example of invertible (m + 1)-isometry which is not an m-isometry. Next we show that if T is an m-isometry, then the operator ΔT,m-1 is not invertible. [ABSTRACT FROM AUTHOR]