Cesàro sequence spaces. (English) Zbl 0568.46006

Lee, Peng Yee

Math. Chron. 13, 29-45 (1984).

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)

Keywords:

sequence spaces; Cesàro matrix; dual spaces; matrix transformations; function spaces