Abstract. We consider the isometric equivalence problem for various classical matrix operators on $l^p$. We extend some of these results to invertible operator weighted shifts on $l^p({\cal H})$, $1\leq p< \infty$, where $\cal H$ is a complex Hilbert space. Furthermore, we consider the isometric equivalence problem for the Cesàro operator on rearrangement-invariant function spaces.

AMS Subject Classification (1991): 47A05, 47B37, 47B49

Received July 12, 2005, and in final form February 24, 2006. (Registered under 5919/2009.)