m¡ISOMETRIC ELEMENTS OF C¤¡ALGEBRAS

An element a in the unital C¤-algebra A is said to be an m¡isometry if Xm k=0 (¡1)m¡k( m k )a¤kak = 0; m 2 N: In this paper, we prove that power bounded m¡isometries are, in fact, isometries.