Bulletin of the Belgian Mathematical Society - Simon Stevin

Invariant Subspaces Of Toeplitz Operators And Uniform Algebras

Takahiko Nakazi

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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

Permanent link to this document
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

Keywords
Toeplitz operator invariant subspace analytic symbol

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


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