Research Article
Minimal Reducing Subspaces of 3-order Slant Toeplitz Operator on Hardy Space over the Disc
Yang Zou*
Issue:
Volume 11, Issue 1, March 2025
Pages:
1-9
Received:
9 January 2025
Accepted:
26 January 2025
Published:
17 February 2025
DOI:
10.11648/j.ml.20251101.11
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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.
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 ...
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