Scholarlink

In this article, we are interested in finding new norm inequalities for block accretive-dissipative matrices that compare the diagonal blocks with the off diagonal blocks. Moreover, given the partitioned positive semi-definite matrix \(T=\left[ \begin{array}{cc}A & X\\ X^{*} & B \end{array} \right] \) , we prove that \( \left\| T\right\| _{u}\le \left\| A+B\right\| _{u}+2w_{u}(X) \) for any unitarily invariant norm \(\left\| \cdot \right\| _{u}\) , where \(w_{u}(\cdot )\) is the generalized numerical radius induced by \(\left\| \cdot \right\| _{u}\) .

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Norm Inequalities Involving Accretive-Dissipative Matrices

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Aref Sarhan,
  • Aliaa Burqan

摘要

In this article, we are interested in finding new norm inequalities for block accretive-dissipative matrices that compare the diagonal blocks with the off diagonal blocks. Moreover, given the partitioned positive semi-definite matrix \(T=\left[ \begin{array}{cc}A & X\\ X^{*} & B \end{array} \right] \) , we prove that \( \left\| T\right\| _{u}\le \left\| A+B\right\| _{u}+2w_{u}(X) \) for any unitarily invariant norm \(\left\| \cdot \right\| _{u}\) , where \(w_{u}(\cdot )\) is the generalized numerical radius induced by \(\left\| \cdot \right\| _{u}\) .