Properties of H-Toeplitz operators on the bidisk Bergman space

Jingwen Duan; Bo Zhang; Yinghui Liu; Jingwen Duan; Bo Zhang; Yinghui Liu

doi:10.3934/math.2026937

AIMS Mathematics

2026, Volume 11, Issue 7: 23234-23261. doi: 10.3934/math.2026937

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Research article

Properties of H-Toeplitz operators on the bidisk Bergman space

School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China

Received: 28 April 2026 Revised: 10 July 2026 Accepted: 16 July 2026 Published: 30 July 2026
MSC : 47B35, 46E20

This paper investigated H-Toeplitz operators on the bidisk Bergman space $ L_a^2(\mathbb{D}^{2}) $. First, we provided the matrix-type representation for the H-Toeplitz operator $ B_\phi $. Next, we presented the necessary and sufficient conditions for such operators to be co-isometries and partial isometries. Then, we proved that any diagonal H-Toeplitz operator with some pluriharmonic symbol must be the zero operator. Finally, we characterized several invariant subspaces and kernel spaces associated with H-Toeplitz operators.
- bidisk Bergman space,
- H-Toeplitz operators,
- partial isometry,
- invariant subspaces,
- kernel spaces
Citation: Jingwen Duan, Bo Zhang, Yinghui Liu. Properties of H-Toeplitz operators on the bidisk Bergman space[J]. AIMS Mathematics, 2026, 11(7): 23234-23261. doi: 10.3934/math.2026937

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Abstract

This paper investigated H-Toeplitz operators on the bidisk Bergman space $ L_a^2(\mathbb{D}^{2}) $. First, we provided the matrix-type representation for the H-Toeplitz operator $ B_\phi $. Next, we presented the necessary and sufficient conditions for such operators to be co-isometries and partial isometries. Then, we proved that any diagonal H-Toeplitz operator with some pluriharmonic symbol must be the zero operator. Finally, we characterized several invariant subspaces and kernel spaces associated with H-Toeplitz operators.

References

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