Asymptotic behaviours and generalized Toeplitz operators
by
Laurian Suciu
Department of Mathematics, West University of Timisoara, Romania
Coauthors: Nicolae Suciu

We study some generalized Toeplitz operators associated to operators T on a Hilbert space H, for which the limit of ||Tⁿh|| exists for every h ∈ H. We refer to the asymptotic limit S_T of such a T, in the sense of Kerchy, Cassier, Kubrusly and we give some conditions of ergodicity for T. Also, certain results of Douglas involving generalized Toeplitz operators are extended in our more general setting, and we apply these results to r-contractions.

Date received: June 9, 2008