Blum-Hanson property and quasisimilarity of operators
by
Vladimir Muller
Mathematical Institute, Czech Academy of Sciences, Prague
Coauthors: Yu. Tomilov

Let T be a contraction on a Hilbert space H such that Tⁿ converges in the weak operator theory. By a result motivated by ergodic theory then T has the Blum-Hanson property, i.e., lim_N→∞N^-1∑_n=1^N T^k_nx exists in the norm topology for each x ∈ H and each increasing subsequence (k_n). We show that this is not true for power bounded Hilbert space operators. This also implies that there are power bounded operators which are not quasisimilar to a contraction.

Date received: May 2, 2008