Let X be a complex Banach space. The connection between algebra homomorphisms defined on subalgebras of the Banach algebra l (1)(N-0) and fractional versions of CesA ro sums of a linear operator T a B(X) is established. In particular, we show that every (C, alpha)-bounded operator T induces an algebra homomorphism - and it is in fact characterized by such an algebra homomorphism. Our method is based on some sequence kernels, Weyl fractional difference calculus and convolution Banach algebras that are introduced and deeply examined. To illustrate our results, improvements to bounds for Abel means, new insights on the (C, alpha)-boundedness of the resolvent operator for temperated a-times integrated semigroups, and examples of bounded homomorphisms are given in the last section.
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机译：令X为复杂的Banach空间。建立了在Banach代数l（1）（N-0）的子代数上定义的代数同构与线性算子T a B（X）的CesA ro和的分数形式之间的联系。特别是，我们证明了每个（C，α）界算子T都诱导出一个代数同态-实际上它的特征是这种代数同态。我们的方法是基于一些序列核，Weyl分数差分微积分和卷积Banach代数进行介绍和深入研究的。为了说明我们的结果，改进了Abel的边界，在上一节中给出了对温度为a的积分半群的解析算子的（C，alpha）有界性的新见解，以及有界同态的示例。
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