Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-09-06 , DOI: 10.1080/03081087.2020.1810201 Nirmal Chandra Rout 1 , Satyajit Sahoo 2 , Debasisha Mishra 1
Let be a complex Hilbert space, and A be a positive bounded linear operator on Let denote the set of all bounded linear operators on whose A-adjoint exists. Let denote a operator matrix of the form . Very recently, for a strictly positive operator A, Bhunia et al. [On inequalities for A-numerical radius of operators. Electron J Linear Algebra. 2020;36:143–157] proved an important lemma (Lemma 2.4) to establish several -numerical radius inequalities for operator matrices in . In this article, we first prove an analogous result and then provide a new proof of the same lemma by dropping the assumption ‘A is strictly positive’. We then establish several new upper and lower bounds for the -numerical radius of an operator matrix whose entries are operators in Further, we prove some refinements of earlier A-numerical radius inequalities for operators in .
中文翻译:
关于 2 × 2 算子矩阵的 𝔸-数值半径不等式
让是一个复希尔伯特空间,并且A是一个正有界线性算子让表示所有有界线性算子的集合其A -伴随存在。让表示一个形式的算子矩阵. 最近,对于严格的正算子A,Bhunia 等人。[关于算子的A数值半径的不等式。电子 J 线性代数。2020;36:143–157] 被证明是一个重要的引理(引理 2.4),可以建立几个-算子矩阵的数值半径不等式. 在本文中,我们首先证明了一个类似的结果,然后通过放弃“ A严格为正”的假设来提供相同引理的新证明。然后我们为- 一个算子矩阵的数值半径,其条目是算子此外,我们证明了早期A数值半径不等式的一些改进.