Matrix-Valued Truncated Toeplitz Operators: Unbounded Symbols, Kernels and Equivalence After Extension
Matrix-Valued Truncated Toeplitz Operators: Unbounded Symbols, Kernels and Equivalence After Extension
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矩阵值截断托普利茨算子：扩展后的无界符号、核和等价
DOI：
10.1007/s00020-022-02685-5
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发表时间：
2022
影响因子：
0.8
通讯作者：
O'Loughlin R
中科院分区：
文献类型：
--
作者：
O'Loughlin R
本文研究矩阵值截断Toeplitz算子，它是截断Toeplitz算子的向量推广.证明了，虽然存在矩阵值截断Toeplitz算子，但对于任意的情形，都存在一类矩阵值截断Toeplitz算子，并且对于某些情形，都存在一类矩阵值截断Toeplitz算子.在矩阵值截断Toeplitz算子的符号为的情况下，开发了一种方法，该方法绕过了处理具有无界符号的矩阵值截断Toeplitz算子问题时出现的一些技术困难。使用这种新方法，得到了两个新的显着结果。矩阵值截断Toeplitz算子的核表示为非不变子空间的等距像。此外，构造了一个Toeplitz算子，它是等价的矩阵值截断Toeplitz算子的扩展后。在一个不同的，但重叠的静脉，它也表明，多维类似物的截断维纳-霍普夫运营商是酉等价于某些矩阵值截断Toeplitz运营商。
This paper studies matrix-valued truncated Toeplitz operators, which are a vectorial generalisation of truncated Toeplitz operators. It is demonstrated that, although there exist matrix-valued truncated Toeplitz operators without a matrix symbol infor any, there is a wide class of matrix-valued truncated Toeplitz operators which possess a matrix symbol infor some. In the case when the matrix-valued truncated Toeplitz operator has a symbol infor some, an approach is developed which bypasses some of the technical difficulties which arise when dealing with problems concerning matrix-valued truncated Toeplitz operators with unbounded symbols. Using this new approach, two new notable results are obtained. The kernel of the matrix-valued truncated Toeplitz operator is expressed as an isometric image of an-invariant subspace. Also, a Toeplitz operator is constructed which is equivalent after extension to the matrix-valued truncated Toeplitz operator. In a different yet overlapping vein, it is also shown that multidimensional analogues of the truncated Wiener–Hopf operators are unitarily equivalent to certain matrix-valued truncated Toeplitz operators.
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DOI：
--
发表时间：
1992
期刊：
影响因子：
--
作者：
H. Bart;V. E. Tsekanovskii
通讯作者：
V. E. Tsekanovskii
有界平均振荡的径向极限和星不变子空间
影响因子：
1.7
作者：
W. Cohn
通讯作者：
W. Cohn
向量值 Hardy 空间上移位算子的几乎不变子空间
影响因子：
0.8
作者：
A. Chattopadhyay;Soma Das;Chandan Pradhan
通讯作者：
Chandan Pradhan
双频带通用 Toeplitz 算子
影响因子：
1.1
作者：
M. Câmara;Ryan O’Loughlin;J. Partington
通讯作者：
J. Partington
用于块 Toeplitz 算子的标量型内核
影响因子：
1.3
作者：
M. Cristina Câmara;J. Partington
通讯作者：
J. Partington