Abstract. $AC$-operators were introduced by Berkson and Gillespie as a generalization in the context of well-boundedness of normal operators on Hilbert space. In this paper we explore some of the properties of these operators, such as the uniqueness of their splitting into real and imaginary parts, and their interpolation properties. We also examine the interpolation properties of the important subclass consisting of the trigonometrically well-bounded operators.

AMS Subject Classification (1991): 47B40, 46B70

Keyword(s): AC, -operators, trigonometrically well-bounded operators, functional calculus, interpolation properties

Received March 29, 1996. (Registered under 6113/2009.)