论文标题
矩阵值截断的toeplitz运算符：扩展后的无限符号，内核和等价
Matrix-valued truncated Toeplitz operators: unbounded symbols, kernels and equivalence after extension
论文作者
论文摘要
本文研究了矩阵值截断的toeplitz运算符，这是截短的toeplitz oberators的矢量概括。证明，尽管存在矩阵值截断的toeplitz运算符，而在$ l^p $中没有矩阵符号的任何$ p $（2，\ infty] $中的任何$ p \，但在$ l^p $ for $ p \ for $ p \ in（2，\ infty] $中，有一类矩阵的toeplitz toeplitz toeplitz epplitz epplitz符号in $ p $ for $ p \ in $ p \ in（2，in 2，in 2，in 2，in 2，in（2，in）。 matrix-valued truncated Toeplitz operator has a symbol in $L^p$ for some $p \in (2, \infty ]$, 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 $S^*$-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单位等同于某些矩阵值截断的toeplitz操作员。
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 in $L^p$ for any $p \in (2, \infty ]$, there is a wide class of matrix-valued truncated Toeplitz operators which possess a matrix symbol in $L^p$ for some $p \in (2, \infty ]$. In the case when the matrix-valued truncated Toeplitz operator has a symbol in $L^p$ for some $p \in (2, \infty ]$, 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 $S^*$-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.
