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oai:docta.ucm.es:20.500.14352/717172024-07-12T14:25:44Zcom_20.500.14352_14col_20.500.14352_15

Insights on the Cesàro operator: shift semigroups and invariant subspaces Gallardo Gutiérrez, Eva Antonia Partington, Johathan R. 517.98 Cesàro operator Composition operator Shift semigroup Invariant subspaces Functional calculus Análisis matemático 1202 Análisis y Análisis Funcional A closed subspace is invariant under the Cesàro operator C on the classical Hardy space H2 (D) if and only if its orthogonal complement is invariant under the C0-semigroup of composition operators induced by the affine maps φt(z) = e−t z + 1 − e −t for t ≥ 0 and z ∈ D. The corresponding result also holds in the Hardy spaces Hp(D) for 1 < p < ∞. Moreover, in the Hilbert space setting, by linking the invariant subspaces of C to the lattice of the closed invariant subspaces of the standard right-shift semigroup acting on a particular weighted L 2 -space on the line, we exhibit a large class of non-trivial closed invariant subspaces and provide a complete characterization of the finite codimensional ones, establishing, in particular, the limits of such an approach towards describing the lattice of all invariant subspaces of C. Finally, we present a functional calculus which allows us to extend a recent result by Mashreghi, Ptak and Ross regarding the square root of C and discuss its invariant subspaces. Ministerio de Ciencia e Innovación (MICINN) Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas FALSE unpub 2023-06-22T10:48:56Z 2023-06-22T10:48:56Z 2022-06 journal article https://hdl.handle.net/20.500.14352/71717 XXXX-XXXX eng PID2019-105979GB-I00 CEX2019-000904-S 20205CEX001 Atribución 3.0 España https://creativecommons.org/licenses/by/3.0/es/ open access application/pdf