Bulletin of the Australian Mathematical Society

Research Article

A structure theorem for operators with closed range

James Guykera1

a1 Department of Mathematics, State University of New York, College at Buffalo, Buffalo, New York, USA.


A characterization has previously been given for linear transformations in Hilbert space whose first N + 1 powers are partial isometries. An analogous characterization is now obtained for transformations whose first N+ 1 powers have closed ranges. A hypothesis (that transformations have no isometric part) is found to be unnecessary in previous work.

(Received November 15 1977)