Abstract. In this paper we investigate linear operators between certain sequence spaces $X$ and $Y$. Among other things, if $X$ is any $p$--normed space and $Y = w_0^1, w^1, w_{\infty }^1, c_0(\mu ), c(\mu )$, or $c_{\infty }(\mu )$ we find necessary and sufficient conditions for $A$ to map $X$ into $Y$. Then the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.

AMS Subject Classification (1991): 40H05, 46A45, 47B07

Keyword(s): BK spaces, bases, matrix transformations, measure of noncompactness

Received February 28, 1997 and in revised form October 20, 1997. (Registered under 2653/2009.)