Gallardo Gutiérrez, Eva AntoniaMonsalve López, Miguel2025-12-152025-12-152021Gallardo-Gutiérrez, E.A., Monsalve-López, M. Spectral Decompositions Arising from Atzmon’s Hyperinvariant Subspace Theorem. Integr. Equ. Oper. Theory 93, 6 (2021)10.1007/s00020-020-02618-0https://hdl.handle.net/20.500.14352/129027By means of a weaker functional model, we prove the existence of non-trivial closed hyperinvariant subspaces for linear bounded operators generalizing, in particular, a classical theorem of Atzmon and revealing the spectral nature of the hyperinvariant subspaces involved. As an application, we show non-trivial spectral subspaces for Bishop operators on $L^p[0,1)$, $1 \leq p < \infty$, as long as they satisfy Atzmon’s Theorem, providing, in turns, a local spectral decomposition.engjournal articlehttps://doi.org/10.1007/s00020-020-02618-0open accessHyperinvariant subspacesInvariant subspacesBishop operatorsSpectral decompositionAnálisis funcional y teoría de operadores1202.03 Álgebra y Espacios de Banach1202.14 Espacio de Hilbert