Invariant subspaces with no generator and a problem of H. Helson
Annales de l'Institut Fourier, Volume 65 (2015) no. 4, p. 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 : https://doi.org/10.5802/aif.2964
Classification:  43A17,  46J10,  46J15,  28D10
Keywords: Compact groups with ordered duals, Invariant subspaces, Cocycles, Single generators 
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {4},
     year = {2015},
     pages = {1469-1491},
     doi = {10.5802/aif.2964},
     zbl = {1332.43002},
     language = {en},
     url = {http://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, Volume 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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