RT Journal Article
T1 Regular fractional weighted Wiener algebras and invariant subspaces
A1 Abadias, Luciano
A1 Monsalve López, Miguel
AB Since the fififties, 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 $\mathcal{A}_\rho^\alpha$ related with the Cesàro summation of order $\alpha \geq 0$. At the end of the article, other summability methods are considered for the purpose of fifinding new sufficient criteria which ensure the existence of invariant subspaces, resulting in several open questions on the regularity of fractional weighted Wiener algebras $\mathcal{A}_\rho^\mu$ associated to matrix summation methods defifined from non-vanishing complex sequences.
PB Elsevier
YR 2026
FD 2026
LK https://hdl.handle.net/20.500.14352/129006
UL https://hdl.handle.net/20.500.14352/129006
LA eng
NO Abadias, L., Monsalve-L\'opez, M., Regular fractional weighted Wiener algebras and invariant subspaces, J. Math. Anal. Appl. 553 (2026), no. 2, Paper No. 129875.
NO 2025 Acuerdos transformativos CRUE
NO Ministerio de Ciencia e Innovación (España) 
NO Gobierno de Aragón
DS Docta Complutense
RD 21 mar 2026