Abstract. We determine the continuous duals of the spaces of $\Lambda $-strongly null and $\Lambda $-strongly convergent sequences for nondecreasing exponentially bounded sequences $\Lambda $ of positive reals tending to infinity. This is a partial solution of the problem by Móricz in [2].

AMS Subject Classification (1991): 40H05

Received December 19, 1994, and in revised form February 8, 1995. (Registered under 5683/2009.)