论文标题
疟疾矩阵
Malnormal matrices
论文作者
论文摘要
我们展示了一个运算符规范，无限序列$ \ {a_n \} $ $ 3n \ times 3n $复杂矩阵的换向器映射$ x \ mapsto xa_n-a_nx $在带有带有Trace-Zero自动选择矩阵的零件自动选择矩阵的操作员下面均匀地限制在下面，该操作员配备了Hillibers-schmidt stard。该构建基于量子扩张器的家族。我们在量子扩张器的研究中提供了这些矩阵的几种潜在应用。我们制定了几种与此类矩阵有关的自然猜想和问题，并提供了数值证据。
We exhibit an operator norm bounded, infinite sequence $\{A_n\}$ of $3n \times 3n$ complex matrices for which the commutator map $X\mapsto XA_n - A_nX$ is uniformly bounded below as an operator over the space of trace-zero self-adjoint matrices equipped with Hilbert--Schmidt norm. The construction is based on families of quantum expanders. We give several potential applications of these matrices to the study of quantum expanders. We formulate several natural conjectures and problems related to such matrices and provide numerical evidence.
