In this note, we study invariant subspaces of $L^2(\Bbb T^2)$ with respect to certain von Neumann algebras. We give a characterization of Beurling-type left-invariant subspaces of $L^2(\Bbb T^2)$. We also give a structure theorem of a non-trivial two-sided invariant subspace of $L^2(\Bbb T^2)$.
Publié le : 2006-08-15
Classification:
von Neumann algebras,
invariant subspaces,
Popovici's decomposition,
46L10,
47A15
@article{1285766419,
author = {HASEGAWA, Atsushi},
title = {The invariant subspace structure of $L^2(\Bbb T^2)$ for certain von Neumann algebras},
journal = {Hokkaido Math. J.},
volume = {35},
number = {1},
year = {2006},
pages = { 601-611},
language = {en},
url = {http://dml.mathdoc.fr/item/1285766419}
}
HASEGAWA, Atsushi. The invariant subspace structure of $L^2(\Bbb T^2)$ for certain von Neumann algebras. Hokkaido Math. J., Tome 35 (2006) no. 1, pp. 601-611. http://gdmltest.u-ga.fr/item/1285766419/