Article
Invariant subspaces of parabolic self-maps in the Hardy space
Author/s | Montes Rodríguez, Alfonso
![]() ![]() ![]() ![]() ![]() ![]() Ponce Escudero, Manuel Shkarin, Stanislav A. |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Date | 2010-01 |
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Abstract | It is shown that the lattice of invariant subspaces of the operator of multiplication by a cyclic element of a Banach algebra consists of the closed
ideals of this algebra. As an application, with the help of some elements ... It is shown that the lattice of invariant subspaces of the operator of multiplication by a cyclic element of a Banach algebra consists of the closed ideals of this algebra. As an application, with the help of some elements of the Gelfand Theory of Banach algebras, the lattice of invariant subspaces of composition operators acting on the Hardy space, whose inducing symbol is a parabolic non-automorphism, is found. In particular, each invariant subspace always consists of the closed span of a set of eigenfunctions. As a consequence, such composition operators have no non-trivial reducing subspaces. |
Funding agencies | Ministerio de Ciencia y Tecnología (MCYT). España Junta de Andalucía |
Project ID. | BFM2003-00034
![]() FQM-260 ![]() |
Citation | Montes Rodríguez, A., Ponce Escudero, M. y Shkarin, S.A. (2010). Invariant subspaces of parabolic self-maps in the Hardy space. Mathematical Research Letters, 17 (1), 99-107. |
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