162265 20251017144559.0 doi 10.1016/j.jmaa.2025.129875 sideral 144636 ART-2026-144636 eng Abadías Ullod, Luciano Universidad de Zaragoza (orcid)0000-0003-2453-7841 Regular fractional weighted Wiener algebras and invariant subspaces 2026 Access copy available to the general public Unrestricted Since the fifties, the interplay between spectral theory, harmonic analysis and a wide variety of techniques based on the functional calculus of operators, has provided useful criteria to find non-trivial closed invariant subspaces for operators acting on complex Banach spaces. In this article, some standard summability methods (mainly the Cesàro summation) are applied to generalize classical results due to Wermer [51] and Atzmon [8] regarding the existence of invariant subspaces under growth conditions on the resolvent of an operator. To do so, an extension of Beurling's regularity criterion [13] is proved for fractional weighted Wiener algebras related with the Cesàro summation of order . At the end of the article, other summability methods are considered for the purpose of finding new sufficient criteria which ensure the existence of invariant subspaces, resulting in several open questions on the regularity of fractional weighted Wiener algebras associated to matrix summation methods defined from non-vanishing complex sequences. info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Monsalve-López, Miguel 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 553, 2 (2026), 129875 [35 pp.] J. math. anal. appl. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 0022-247X 698367 http://zaguan.unizar.es/record/162265/files/texto_completo.pdf Versión publicada 1805702 http://zaguan.unizar.es/record/162265/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:162265 articulos driver 2025-10-17-14:13:50 ARTICLE