Vol. 57, No. 2, 1975

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Hyponormal contractions and strong power convergence

Calvin R. Putnam

Vol. 57 (1975), No. 2, 531–538
Abstract

Let T be a hyponormal contraction on a Hilbert space, so that TTTT = D 0 and T1. 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
Authors
Calvin R. Putnam