Hokkaido Mathematical Journal

RHOADES B.E.,

Some sequence spaces which include $c_0$ and $c$.

Hokkaido Mathematical Journal, 35 (2006) pp.587-599

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Abstract

It is first shown that a certain class of regular factorable matrices is equivalent to $C$, the Ces\'{a}ro matrix of order one. As a corollary it is shown that the matrix $A$ of [1] is equivalent to $C$. Then most of the results of [1] and [3] are extended to regular factorable matrices.

MSC(Primary)46A35
MSC(Secondary)46A45, 46B45
Uncontrolled Keywords$\alpha$ dual, $\beta$ dual, Ces\'{a}ro summability, $\gamma$ dual, factorable matrices, $\ell_p$ spaces, weighted mean matrices