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Abstract. We characterize those sequences $\left\{h_n \right\} _{n=1}^{\infty }$ of bounded analytic functions, which have the property that an absolutely continuous contraction $T$ is stable (that is the powers $T^n$ converge to zero) exactly when the operators $h_n(T)$ converge to zero in the strong operator topology. Our result is extended to polynomially bounded operators too.
AMS Subject Classification
(1991): 47A60, 47A45
Keyword(s):
stability,
contraction,
polynomially bounded operator,
functional calculus
Received May 29, 2012, and in revised form December 22, 2012. (Registered under 41/2012.)
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