Hyponormal contractions and strong power convergence

Calvin R. Putnam

Vol. 57 (1975), No. 2, 531–538

DOI: 10.2140/pjm.1975.57.531

Abstract

Let T^∗ be a hyponormal contraction on a Hilbert space, so that TT^∗−T^∗T = D ≧ 0 and ∥T∥≦ 1. It is shown that if, in addition, T^∗ is completely hyponormal, then the sequence {Tⁿ}_n=1.2,⋯ converges strongly to 0 as n →∞. The result is obtained as a consequence of properties of the solution w(z) of (T −zI)w(z) = x, where x is a certain vector in the range of D.

Mathematical Subject Classification 2000

Primary: 47B20

Milestones

Received: 27 November 1974

Published: 1 April 1975