Cesàro sums and algebra homomorphisms of bounded operators

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• 作者：Luciano Abadias ; Carlos Lizama ; Pedro J. Miana…
• 刊名：Israel Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：216
• 期：1
• 页码：471-505
• 全文大小：370 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511
• 卷排序：216

文摘

Let X be a complex Banach space. The connection between algebra homomorphisms defined on subalgebras of the Banach algebra l1(N₀) and fractional versions of Cesàro sums of a linear operator T ∈ B(X) is established. In particular, we show that every (C, α)-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, α)-boundedness of the resolvent operator for temperated a-times integrated semigroups, and examples of bounded homomorphisms are given in the last section.