Invariant subspaces with no generator and a problem of H. Helson
Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1469-1491.

In the almost-periodic context, the H 0 2 -space cannot be generated by one of its elements. Together with a cocycle argument, this implies that there exist all kinds of invariant subspaces without a single generator, from which we answer some questions on invariant subspace theory.

Dans le contexte presque périodique, aucun espace H 0 2 ne peut être engendré par un de ses éléments. En tenant compte d’un argument faisant intervenir les cocycles, on peut en déduire qu’il existe de nombreux types de sous-espaces invariants qui ne peuvent pas être engendrés par un seul de leurs éléments ; ceci permet de répondre à quelques questions de la théorie des sous-espaces invariants.

DOI: 10.5802/aif.2964
Classification: 43A17, 46J10, 46J15, 28D10
Keywords: Compact groups with ordered duals, Invariant subspaces, Cocycles, Single generators
Mot clés : Groupes compactes avec dualité ordonnée, sous-espaces invariants, cocycles, générateurs singulier
Tanaka, Jun-ichi 1

1 Department of Mathematics, School of Education, Waseda University, Shinjuku, Tokyo 169-8050 (Japan)
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Tanaka, Jun-ichi. Invariant subspaces with no generator  and a problem of H. Helson. Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1469-1491. doi : 10.5802/aif.2964. https://aif.centre-mersenne.org/articles/10.5802/aif.2964/

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