Abstract. The $\alpha $-duals of the sequence spaces $w_{\infty } (p)$ and $w_{0}(p)$ were determined in [2], Satz 8, p. 79, and [1], Th. 4, p. 103 for $p_{k}\le1$ ($k=1,2,\ldots$). Nothing seems to be known in the case $p_{k}>1$ ($k=1,2,...$) except when $p_{k}=p>1$ for all $k$ (cf. [3]). Here we shall determine the $\alpha $-duals of $w_{\infty }(p)$ and $w_{0}(p)$ in some cases where $p_{k}>1$ ($k=1,2,...$).

AMS Subject Classification (1991): 40H05

Keyword(s): sequence spaces, dual spaces

Received September 19, 1994, in revised form February 8, 1995. (Registered under 5650/2009.)