一些新的α阶塞萨罗序列空间

Pub Date : 2024-09-06 DOI:10.1007/s11253-024-02333-8

Medine Yeşilkayagil Savaşcı, Feyzi Başar

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引用次数: 0

摘要

我们分别引入阶为 α 的 Cesàro 有界序列、Cesàro 几乎收敛序列和 Cesàro 几乎无效序列的空间 ℓ∞(𝒞α)、f(𝒞α) 和 f0(𝒞α)。此外，我们还为这些空间建立了一些包含关系，并确定了空间 ℓ∞ (𝒞α) 和 f(𝒞α) 的 α -、β - 和 γ 二重。最后，我们描述了从空间 f(𝒞α) 到任意序列空间 Y 以及从任意序列空间 Y 到空间 f(𝒞α) 的矩阵变换类。

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Some New Cesàro Sequence Spaces of Order α

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).

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