On p-Numerical Radius Inequalities for Hilbert Space Operators

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-08-07 Epub Date: 2026-07-06 DOI:10.1002/mana.70187

Fugen Gao, Mengyu Hou, Jie Zhao

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引用次数: 0

Abstract

This paper introduces novel inequalities for the $p$ -numerical radius of operators. Among our main findings, we prove that

\begin{matrix} w_{p} (T) \leq 2^{\frac{1}{p} - 1} \min_{t \in (0, 1)} (w_{p} ({\tilde{T}}_{t}) + \sqrt{{∥ | T |}^{2 t} ∥_{p} {∥ | T |}^{2 (1 - t)} ∥_{p}}), \end{matrix}

for

1 \leq p \leq \infty

, where

{\tilde{T}}_{t} = {| T |}^{t} U {| T |}^{1 - t}

denotes the generalized Aluthge transform of

T

. These inequalities refine and extend several existing bounds in the literature. Furthermore, we investigate the

p

-numerical radius of several significant classes of

2 \times 2

operator matrices.

查看原文本刊更多论文

Hilbert空间算子的p数值半径不等式

本文引入了算子p $p$ -数值半径的新不等式。在我们的主要发现中，我们证明了w p T≤2 1 p−1 minT∈0，1 w p (T ～ T) +∥| t |T∥p∥|2(1−T) p；$$\begin{align*} {w_p}{\left(T \right)} \le {2^{\frac{1}{p} - 1}} \mathop {\min }\limits _{t \in {\left[ {0,1} \right]}}{\left\lbrace {w_p}({{\tilde{T}}_{t}})+ \sqrt {\Vert |T|^{2t}\Vert _{p}\Vert |T|^{2(1-t)}\Vert _{p}}\right\rbrace}, \end{align*}$$对于1≤p≤∞$1 \le p \le \infty$，

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index