## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Invariant Subspaces Of Toeplitz Operators And Uniform Algebras

Takahiko Nakazi

#### Abstract

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 $H^2$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 1 (2008), 1-8.

Dates
First available in Project Euclid: 22 February 2008

https://projecteuclid.org/euclid.bbms/1203692442

Digital Object Identifier
doi:10.36045/bbms/1203692442

Mathematical Reviews number (MathSciNet)
MR2406082

Zentralblatt MATH identifier
1147.47023

Subjects
Primary: 47 B 35 47 A 15
Secondary: 46 J 15

#### Citation

Nakazi, Takahiko. Invariant Subspaces Of Toeplitz Operators And Uniform Algebras. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 1, 1--8. doi:10.36045/bbms/1203692442. https://projecteuclid.org/euclid.bbms/1203692442