Abstract. We obtain some intrinsic algebraic characterizations of Hilbert space operators which are similar to elements of some classes of power partial isometries. A power partial isometry is a partial isometry, all whose powers are also partial isometries. We study operators which are similar to direct sums whose summands are finite sums of truncated shifts, isometries or coisometries, as well as operators similar to subnormal or normal partial isometries.

AMS Subject Classification (1991): 47A05, 47A62

Received February 2, 2007, and in revised form July 21, 2008. (Registered under 6038/2009.)