arXiv subjects

Kangjian Wu

Publications and source records attributed to Kangjian Wu.

3 recordsLinked to original sources

arXiv2026

Norm attainment of a class of block operator matrices

Given complex numbers $a, b, c$ and a non-negative continuous function $φ$ defined on $[0, +\infty)$, consider the $2 \times 2$ matrix $$ M_t = \begin{pmatrix} a & t \\ ct & bφ(t) \end{pmatrix}, \quad t \in [0, +\infty). $$ We establish conditions for the strict monotonicity of the norm function $t \mapsto \|M_t\|$. As an application, we characterize the norm attainment of the corresponding block operator matrix $$ T = \begin{pmatrix} aI_H & A \\ cA^* & bφ(|A|) \end{pmatrix},$$ where $I_H$ is the identity operator on a Hilbert space $H$ and $A$ is a bounded linear operator from another Hilbert space to $H$.

math.FA↗

arXiv2025

The numerical ranges of the generalized quadratic operators

We investigate the generalized quadratic operator defined by $$T =\left( \begin{array}{cc} a I_H & A \\ c A^* & bI_K \end{array} \right) ,$$ where $H$ and $K$ are Hilbert spaces, $A:K\to H$ is a bounded linear operator, $I_H$ and $I_K$ denote the identity operators on $H$ and $K$, respectively, and $a,b,c$ are complex numbers. It is shown that $T$ attains its norm if and only if $A$ attains its norm. Furthermore, a complete characterization of the numerical range of $T$ is provided by a new approach.

math.FA↗

arXiv2025

Convex inequalities in Hilbert $C^*$-modules

The H$\ddot{\rm o}$lder-McCarty inequalities are originally derived in the Hilbert space case and have been generalized via a convex inequality. The main purpose of this paper is to extend this convex inequality to the Hilbert $C^*$-module case, and meanwhile to make some investigations on the H$\ddot{\rm o}$lder-McCarty inequalities in the Hilbert $C^*$-module case.

math.FA↗