Cesàro sums and algebra homomorphisms of bounded operators

Abadías Ullod, Luciano (Universidad de Zaragoza) ; Lizama, Carlos ; Miana, Pedro J. (Universidad de Zaragoza) ; Velasco M. Pilar

Resumen: 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 Ces`aro sums of a linear operator T € 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 alpha-times integrated semigroups, and examples of bounded homomorphisms are given in the last section.

Idioma: Inglés

DOI: 10.1007/s11856-016-1417-3CES

Año: 2016

Publicado en: Israel Journal of Mathematics 216, 1 (2016), 471-505
ISSN: 0021-2172

Factor impacto JCR: 0.796 (2016)

Categ. JCR: MATHEMATICS rank: 105 / 310 = 0.339 (2016) - Q2 - T2

Factor impacto SCIMAGO: 1.487 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2013-42105-P
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P
Financiación: info:eu-repo/grantAgreement/ES/UZ/CUD2014-CIE-09

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)