发表机构
Istanbul Aydin University; George Mason University（伊斯坦布尔阿伊丁大学; 乔治梅森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究矩阵值截断Toeplitz算子的性质，将其应用于Nevanlinna-Pick插值问题，并刻画其酉部分、模型空间不变性及可逆性。
AI 中文摘要
本文中，我们提出了矩阵值截断Toeplitz算子在Nevanlinna-Pick插值问题矩阵版本中的应用。随后，我们研究了由压缩矩阵值符号诱导的矩阵值截断Toeplitz算子的酉部分。我们进一步证明，对于纯矩阵值内函数，相应的模型空间在乘法算子下不变当且仅当该符号为常数。此外，我们利用具有2×2分块矩阵符号的Toeplitz算子，给出了矩阵值非对称截断Toeplitz算子可逆性刻画的代数证明。我们还讨论了矩阵值非对称截断Toeplitz算子的可解性。
英文摘要
In this paper, we present an application of matrix-valued truncated Toeplitz operators to the matrix version of the Nevanlinna-Pick interpolation problem. We then investigate the unitary part of a matrix-valued truncated Toeplitz operator induced by a contractive matrix-valued symbol. We further prove that, for a pure matrix-valued inner function, the corresponding model space is invariant under multiplication operator if and only if the symbol is constant. In addition, we give an algebraic proof of a characterization of the invertibility of matrix-valued asymmetric truncated Toeplitz operators using Toeplitz operators with 2 by 2 block matrix symbol. We also discuss the solvability of matrix-valued asymmetric truncated Toeplitz operators.
