ACTA issues

Characterization of stability of contractions

László Kérchy, Attila Szalai

Acta Sci. Math. (Szeged) 79:1-2(2013), 325-332

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.)