Abstract. We have two typical examples of semi-hyponormal but not hyponormal operators. In this paper, we show that these examples have the following property: Re $\sigma(T) = \sigma(\mathop{\rm Re }T)$.

AMS Subject Classification (1991): 47B20

Received October 24, 1999, and in revised form April 19, 2000. (Registered under 2764/2009.)