Banach Journal of Mathematical Analysis

Reducing subspaces for a class of nonanalytic Toeplitz operators

Jia Deng, Yufeng Lu, Yanyue Shi, and Yinyin Hu

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Abstract

In this paper, we give a uniform characterization for the reducing subspaces for Tφ with the symbol φ(z)=zk+z¯l (k,lZ+2) on the Bergman spaces over the bidisk, including the known cases that φ(z1,z2)=z1Nz2M and φ(z1,z2)=z1N+z¯2M with N,MZ+. Meanwhile, the reducing subspaces for TzN+z¯M (N,MZ+) on the Bergman space over the unit disk are also described. Finally, we state these results in terms of the commutant algebra V(φ).

Article information

Source
Banach J. Math. Anal., Volume 12, Number 2 (2018), 456-480.

Dates
Received: 19 April 2017
Accepted: 29 July 2017
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1513674118

Digital Object Identifier
doi:10.1215/17358787-2017-0035

Mathematical Reviews number (MathSciNet)
MR3779723

Zentralblatt MATH identifier
06873510

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 47C15: Operators in $C^*$- or von Neumann algebras

Keywords
reducing subspace Toeplitz operator Bergman space bidisk von Neumann algebra

Citation

Deng, Jia; Lu, Yufeng; Shi, Yanyue; Hu, Yinyin. Reducing subspaces for a class of nonanalytic Toeplitz operators. Banach J. Math. Anal. 12 (2018), no. 2, 456--480. doi:10.1215/17358787-2017-0035. https://projecteuclid.org/euclid.bjma/1513674118


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References

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