On the uniform ergodic theorem in invariant subspaces

Abstract: Let T be a bounded linear operator on a Banach space X into itself. In this paper, we study the uniform ergodicity of the operator T|Y when Y is a closed subspace invariant under T. We show that if T satisfies , then T is uniformly ergodic on X if and only if the restriction of T to some...

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Autores principales:	Tajmouati,Abdelaziz, Bakkali,Abdeslam El, Fatih,Barki
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Uniform ergodic theorem Cesàro averages decomposition ergodic.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200315
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spelling	oai:scielo:S0716-091720190002003152019-05-30On the uniform ergodic theorem in invariant subspacesTajmouati,AbdelazizBakkali,Abdeslam ElFatih,Barki Uniform ergodic theorem Cesàro averages decomposition ergodic. Abstract: Let T be a bounded linear operator on a Banach space X into itself. In this paper, we study the uniform ergodicity of the operator T\|Y when Y is a closed subspace invariant under T. We show that if T satisfies , then T is uniformly ergodic on X if and only if the restriction of T to some closed subspace Y ⊂ X, invariant under T and R[(I − T)k] ⊂ Y for some integer k ≥ 1, is uniformly ergodic. Consequently, we obtain other equivalent conditions concerning the theorem of Mbekhta and Zemànek ((9), theorem 1), also to the theorem of the Gelfand-Hille type.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.2 20192019-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200315en10.4067/S0716-09172019000200315
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Uniform ergodic theorem Cesàro averages decomposition ergodic.
spellingShingle	Uniform ergodic theorem Cesàro averages decomposition ergodic. Tajmouati,Abdelaziz Bakkali,Abdeslam El Fatih,Barki On the uniform ergodic theorem in invariant subspaces
description	Abstract: Let T be a bounded linear operator on a Banach space X into itself. In this paper, we study the uniform ergodicity of the operator T\|Y when Y is a closed subspace invariant under T. We show that if T satisfies , then T is uniformly ergodic on X if and only if the restriction of T to some closed subspace Y ⊂ X, invariant under T and R[(I − T)k] ⊂ Y for some integer k ≥ 1, is uniformly ergodic. Consequently, we obtain other equivalent conditions concerning the theorem of Mbekhta and Zemànek ((9), theorem 1), also to the theorem of the Gelfand-Hille type.
author	Tajmouati,Abdelaziz Bakkali,Abdeslam El Fatih,Barki
author_facet	Tajmouati,Abdelaziz Bakkali,Abdeslam El Fatih,Barki
author_sort	Tajmouati,Abdelaziz
title	On the uniform ergodic theorem in invariant subspaces
title_short	On the uniform ergodic theorem in invariant subspaces
title_full	On the uniform ergodic theorem in invariant subspaces
title_fullStr	On the uniform ergodic theorem in invariant subspaces
title_full_unstemmed	On the uniform ergodic theorem in invariant subspaces
title_sort	on the uniform ergodic theorem in invariant subspaces
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200315
work_keys_str_mv	AT tajmouatiabdelaziz ontheuniformergodictheoremininvariantsubspaces AT bakkaliabdeslamel ontheuniformergodictheoremininvariantsubspaces AT fatihbarki ontheuniformergodictheoremininvariantsubspaces
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On the uniform ergodic theorem in invariant subspaces

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