论文标题
在操作员，基地和矩阵之间的相互作用上
On interplay between operators, bases, and matrices
论文作者
论文摘要
鉴于可分开的希尔伯特空间上有界的线性运算符$ t $，我们开发了一种方法，允许人们构建具有某些指定代数或渐近结构的$ t $的矩阵表示。我们获得了$ t $的矩阵表示，带有主对角的先签名带，所有矩阵元素的上限，并且具有这些元素的进入式多项式下限和上限。特别是，我们对[46]和其他相关结果的对角线的对角线概括和补充。此外，我们通过Stout（1981）对定理进行了广泛的概括，并（部分）回答了他的公开问题。我们的几个结果在文献中没有类似物。
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations for $T$ with preassigned bands of the main diagonals, with an upper bound for all of the matrix elements, and with entrywise polynomial lower and upper bounds for these elements. In particular, we substantially generalize and complement our results on diagonals of operators from [46] and other related results. Moreover, we obtain a vast generalization of a theorem by Stout (1981), and (partially) answer his open question. Several of our results have no analogues in the literature.
