Dans le contexte presque périodique, aucun espace 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.
In the almost-periodic context, the 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.
Classification : 43A17, 46J10, 46J15, 28D10
Mots clés : Groupes compactes avec dualité ordonnée, sous-espaces invariants, cocycles, générateurs singulier
@article{AIF_2015__65_4_1469_0, author = {Tanaka, Jun-ichi}, title = {Invariant subspaces with no generator and a problem of H. Helson}, journal = {Annales de l'Institut Fourier}, pages = {1469--1491}, publisher = {Association des Annales de l'institut Fourier}, volume = {65}, number = {4}, year = {2015}, doi = {10.5802/aif.2964}, zbl = {1332.43002}, language = {en}, url = {www.numdam.org/item/AIF_2015__65_4_1469_0/} }
Tanaka, Jun-ichi. Invariant subspaces with no generator and a problem of H. Helson. Annales de l'Institut Fourier, Tome 65 (2015) no. 4, pp. 1469-1491. doi : 10.5802/aif.2964. http://www.numdam.org/item/AIF_2015__65_4_1469_0/
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