论文标题
自动接合操作员的对角线I：紧凑的操作员
Diagonals of self-adjoint operators I: compact operators
论文作者
论文摘要
鉴于在可分开的无限维克斯空间上的自动接合运算符$ t $，我们研究了所有可能的对角线的$ t $对角线的$ \ Mathcal d（t）$的问题。对于紧凑型运营商$ t $，我们将对角色Modulo的完整表征为$ t $的内核。也就是说，我们为共享相同非零特征值（具有多重性）与$ t $的运营商类表征了$ \ mathcal d（t）$。此外，我们确定固定紧凑型操作员$ t $的$ \ Mathcal d（t）$，Modulo，用于带有有限维内核的正固定运算符的内核问题。 我们的结果推广了Arveson和Kadison对痕量类正算子的对角线的表征，以及Kaftal，Loreaux和Weiss的紧凑型正算子的对角线。该证明使用对角线至对角线结果的技术，该技术在作者与Siudeja的早期联合作品中率先开创。
Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete characterization of diagonals modulo the kernel of $T$. That is, we characterize $\mathcal D(T)$ for the class of operators sharing the same nonzero eigenvalues (with multiplicities) as $T$. Moreover, we determine $\mathcal D(T)$ for a fixed compact operator $T$, modulo the kernel problem for positive compact operators with finite-dimensional kernel. Our results generalize a characterization of diagonals of trace class positive operators by Arveson and Kadison and diagonals of compact positive operators by Kaftal, Loreaux, and Weiss. The proof uses the technique of diagonal-to-diagonal results, which was pioneered in the earlier joint work of the authors with Siudeja.
