## Cesàro sequence spaces.(English)Zbl 0568.46006

We introduce two classes of sequence spaces, namely, $$X_ p$$ (1$$\leq p\leq \infty)$$ the space of all sequences x such that $$Cx\in \ell_ p$$ and $$cse_ p$$ $$(1<p<\infty)$$ the space of all sequences x such that $$C| x| \in \ell_ p$$ where C is a Cesàro matrix. We characterize among others the dual spaces of these sequence spaces and give two applications to matrix transformations and function spaces respectively.

### MSC:

 46A45 Sequence spaces (including Köthe sequence spaces)