本文综述了谱集与K-谱集的概念，这些概念由John von Neumann引入，用于通过函数的上确界范数估计矩阵函数的范数，并探讨了其在数值线性代数、泛函分析等领域的应用。
摘要：
这是一篇关于谱集的综述，将发表于《线性代数手册》第二版（L. Hogben 编）。由 John von Neumann 引入的谱集和 K-谱集提供了一种通过函数的 sup-范数来估计矩阵函数范数的可能性。这类谱集的例子包括矩阵的数值域或伪谱，这些内容在第16章和第18章中讨论。估计矩阵函数的范数是纯数学和应用数学众多领域中的基本任务，例如（数值）线性代数、泛函分析和数值分析。更具体的例子包括概率论、半群和算子值微分方程的存在性结果、演化方程时间离散化的数值格式研究，或 GMRES 的收敛速度（第41.7节）。谱集的概念涉及线性代数、算子理论、逼近论和复分析之间的许多深层联系。
英文摘要：
This is a survey about spectral sets, to appear in the second edition of Handbook of Linear Algebra (L. Hogben, ed.). Spectral sets and K-spectral sets, introduced by John von Neumann, offer a possibility to estimate the norm of functions of matrices in terms of the sup-norm of the function. Examples of such spectral sets include the numerical range or the pseudospectrum of a matrix, discussed in Chapters 16 and 18. Estimating the norm of functions of matrices is an essential task in numerous fields of pure and applied mathematics, such as (numerical) linear algebra, functional analysis, and numerical analysis. More specific examples include probability, semi-groups and existence results for operator-valued differential equations, the study of numerical schemes for the time discretization of evolution equations, or the convergence rate of GMRES (Section 41.7). The notion of spectral sets involves many deep connections between linear algebra, operator theory, approximation theory, and complex analysis.
Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators
Inequalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators
A note on remotal and uniquely remotal sets in normed linear spaces
Ramakrishna Mission Vivekananda Educational and Research Institute（罗摩克里希那传教士维韦卡南达教育与研究所）；Indian Statistical Institute（印度统计研究所）；Dinabandhu Mahavidyalaya（迪纳班杜学院）
Besov-Lipschitz norm and $p$-energy measure on scale-irregular Vicsek sets
Tsinghua University（清华大学）；Hangzhou Normal University（杭州师范大学）；National University of Defense Technology（国防科技大学）；South China University of Technology（华南理工大学）
A Spectral Characterization of Absolutely Norming Operators on S.N. Ideals
文[6]在任意维复希尔伯特空间上引入了一类绝对赋范算子，文[11]建立了这类算子的谱特征定理。本文将绝对赋范算子的概念推广到各种对称范数。我们建立了复希尔伯特空间上关于各种对称范数绝对赋范的算子的几个谱特征定理。它还表明，对于许多对称规范的绝对赋范运营商有相同的频谱表征证明较早的一类运营商是绝对赋范相对于通常的运营商规范。最后，我们证明了代数$\mathcal B (\mathcal H)$上的对称范数的存在性，即使是单位算子也不能达到它的范数。
