Abstract. In this paper the approximation of a normal operator $A$ on a complex Hilbert space $\cal H$ by positive or self-adjoint operators or by positive contractions is discussed for the operator norm as well as for a norm $|||\cdot |||$ introduced by R.Bouldin. The dimension of the convex set of approximants is computed for both norms. Moreover, those normal operators are characterized for which the approximants in both norms are the same. This extends previously known results of R. Bouldin and of T. Sekiguchi.

AMS Subject Classification (1991): 47A58, 47B15

Received December 28, 1994, and in revised form February 10, 1995. (Registered under 5700/2009.)