Abstract
An operator T on a Banach space X is said to be an (m,)-isometry, if for all xX. In this paper, we study unilateral weighted shift operators which are (m,)-isometries for some integers m. In particular, we show that any power of an (m,)-isometry is not necessarily an (m,)-isometry. We also study strict (3,)-isometries on R2 and give an example of a strict (2n-1,)-isometry on C2, for any odd integer n.