Abstract. In this paper we characterize those positive operators which are asymptotic limits of contractions in strong operator topology or uniform topology. We examine the problem when the asymptotic limits of two contractions coincide.

AMS Subject Classification (1991): 47A45, 47B15, 47B65

Keyword(s): asymptotic limit, contraction, positive operator

Received December 4, 2012. (Registered under 104/2012.)