The reducing subspace problem and the invariant subspace problem of an operator are two core problems in operator theory. There are lots of works on reducing subspaces and invariant subspaces of Toeplitz operators in recent years. A slant Toeplitz operator is a generalization of Toeplitz operator. In this paper, we study minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol zN. By classifying N into three cases, we give a complete description of minimal reducing subspaces. Finally, all minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol zN on the Hardy space of the disc in the complex plane are given. This paper generalizes the relevant results on reducing subspaces of second-order slant Toeplitz Operators, enriches the study of reducing subspaces of slant Toeplitz Operators on Lebesgue spaces, and of the structure of slant Toeplitz Operators.
| Published in | Mathematics Letters (Volume 11, Issue 1) |
| DOI | 10.11648/j.ml.20251101.11 |
| Page(s) | 1-9 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2025. Published by Science Publishing Group |
Hardy Space, 3-order Slant Toeplitz Operators, Minimal Reducing Subspace
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APA Style
Zou, Y. (2025). Minimal Reducing Subspaces of 3-order Slant Toeplitz Operator on Hardy Space over the Disc. Mathematics Letters, 11(1), 1-9. https://doi.org/10.11648/j.ml.20251101.11
ACS Style
Zou, Y. Minimal Reducing Subspaces of 3-order Slant Toeplitz Operator on Hardy Space over the Disc. Math. Lett. 2025, 11(1), 1-9. doi: 10.11648/j.ml.20251101.11
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Download@article{10.11648/j.ml.20251101.11,
author = {Yang Zou},
title = {Minimal Reducing Subspaces of 3-order Slant Toeplitz Operator on Hardy Space over the Disc},
journal = {Mathematics Letters},
volume = {11},
number = {1},
pages = {1-9},
doi = {10.11648/j.ml.20251101.11},
url = {https://doi.org/10.11648/j.ml.20251101.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20251101.11},
abstract = {The reducing subspace problem and the invariant subspace problem of an operator are two core problems in operator theory. There are lots of works on reducing subspaces and invariant subspaces of Toeplitz operators in recent years. A slant Toeplitz operator is a generalization of Toeplitz operator. In this paper, we study minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol zN. By classifying N into three cases, we give a complete description of minimal reducing subspaces. Finally, all minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol zN on the Hardy space of the disc in the complex plane are given. This paper generalizes the relevant results on reducing subspaces of second-order slant Toeplitz Operators, enriches the study of reducing subspaces of slant Toeplitz Operators on Lebesgue spaces, and of the structure of slant Toeplitz Operators.},
year = {2025}
}
TY - JOUR T1 - Minimal Reducing Subspaces of 3-order Slant Toeplitz Operator on Hardy Space over the Disc AU - Yang Zou Y1 - 2025/02/17 PY - 2025 N1 - https://doi.org/10.11648/j.ml.20251101.11 DO - 10.11648/j.ml.20251101.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 1 EP - 9 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20251101.11 AB - The reducing subspace problem and the invariant subspace problem of an operator are two core problems in operator theory. There are lots of works on reducing subspaces and invariant subspaces of Toeplitz operators in recent years. A slant Toeplitz operator is a generalization of Toeplitz operator. In this paper, we study minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol zN. By classifying N into three cases, we give a complete description of minimal reducing subspaces. Finally, all minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol zN on the Hardy space of the disc in the complex plane are given. This paper generalizes the relevant results on reducing subspaces of second-order slant Toeplitz Operators, enriches the study of reducing subspaces of slant Toeplitz Operators on Lebesgue spaces, and of the structure of slant Toeplitz Operators. VL - 11 IS - 1 ER -
School of Mathematics and Big Data, Chongqing University of Education, Chongqing, China
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