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April 2018 Reducing subspaces for a class of nonanalytic Toeplitz operators
Jia Deng, Yufeng Lu, Yanyue Shi, Yinyin Hu
Banach J. Math. Anal. 12(2): 456-480 (April 2018). DOI: 10.1215/17358787-2017-0035

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).

Citation

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Jia Deng. Yufeng Lu. Yanyue Shi. Yinyin Hu. "Reducing subspaces for a class of nonanalytic Toeplitz operators." Banach J. Math. Anal. 12 (2) 456 - 480, April 2018. https://doi.org/10.1215/17358787-2017-0035

Information

Received: 19 April 2017; Accepted: 29 July 2017; Published: April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 06873510
MathSciNet: MR3779723
Digital Object Identifier: 10.1215/17358787-2017-0035

Subjects:
Primary: 47B35
Secondary: 47C15

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 2 • April 2018
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