ABSTRACT

Let (H, 〈 · , · 〉) be a complex Hilbert space and A be a positive bounded linear operator on H. The semi-inner product 〈x, y〉_A: = 〈Ax, y〉, x, y ∈ H, induces a semi-norm $\parallel \cdot {\parallel }_A$ on H. Let ω_A(T) and $\parallel T{\parallel }_A$ denote the A-numerical radius and the A-operator semi-norm of an operator T in semi-Hilbertian space (H, 〈 · , · 〉_A), respectively. In this paper, some new bounds for the A-numerical radius of operators in semi-Hilbertian space are obtained, which improve the existing ones. In particular, a refinement of the triangle inequality for A-operator semi-norm is also shown.

中文翻译：

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半希尔伯特空间算子的 A-数值半径和 A-范数不等式

摘要

设 ( H , < · , · >) 为复数希尔伯特空间，A为H上的正有界线性算子。半内积 < x , y > _A := < Ax , y >, x , y  ∈  H，推导出一个半​​范数$\parallel \cdot {\parallel }_A$在H上。让ω _A ( T ) 和$\parallel 吨{\parallel }_A$分别表示半希尔伯特空间 ( H , 〈 · , · 〉_A ) 中算子T的A -数值半径和A -算子半范数。本文得到了半希尔伯特空间算子的A-数值半径的一些新界，对现有界进行了改进。特别地，还显示了A算子半范数的三角不等式的改进。