Let $T_\phi $ be a Toeplitz operator on the one variable Hardy space $H^2$. We show that if $T_\phi $
has a nontrivial invariant subspace in the set of invariant subspaces of $T_z$ then $\phi $ belongs to $H^\infty $. In
fact, we also study such a problem for the several variables Hardy space $H^2$.
Publié le : 2008-02-15
Classification:
Toeplitz operator,
invariant subspace,
analytic symbol,
47 B 35,
47 A 15,
46 J 15
@article{1203692442,
author = {Nakazi, Takahiko},
title = {Invariant Subspaces Of Toeplitz Operators And Uniform Algebras},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {15},
number = {1},
year = {2008},
pages = { 1-8},
language = {en},
url = {http://dml.mathdoc.fr/item/1203692442}
}
Nakazi, Takahiko. Invariant Subspaces Of Toeplitz Operators And Uniform Algebras. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp. 1-8. http://gdmltest.u-ga.fr/item/1203692442/