Some New Cesàro Sequence Spaces of Order α

Abstract

We introduce the spaces ℓ_∞(𝒞_α), f(𝒞_α), and f₀(𝒞_α) of Cesàro bounded, Cesàro almost convergent, and Cesàro almost null sequences of order α, respectively. Moreover, we establish some inclusion relations for these spaces and determine the α -, β- and γ-duals of the spaces ℓ_∞ (𝒞_α) and f(𝒞_α). Finally, we characterize the classes of matrix transformations from the space f(𝒞_α) to any sequence space Y and from any sequence space Y to the space f(𝒞_α).