论文标题
$ \ mathbb {a} $ - 数字半径不等式的进一步结果
Further results on $\mathbb{A}$-numerical radius inequalities
论文作者
论文摘要
让$ a $为复杂的希尔伯特空间上的有界线性正面操作员$ \ mathcal {h}。$，此外，让$ \ m artercal {b} _a \ nathcal {（h）} $表示所有限制的线性操作员的集合，上$ \ nathcal {h} $ - $ \ mathbb {a} $表示具有对角线条目的对角线操作员矩阵。 2020年]和Bhunia {\ it等} [线性多线性代数（2020），doi：10.1080/03080/03080/03087.2020.1781037] $ \ MATHCAL {B} _A（\ MATHCAL {H}）$和“ $ A $是严格的正面”。 在本文中，我们证明了一些新的$ \ mathbb {a} $ - 数字半径不平等，价格为$ 2 \ times 2 $和$ n \ times n $ ocerator矩阵。我们还通过放松不同的足够条件（例如“ $ \ Mathcal {n}（a）（a）^\ perp $在不同的操作员下是不变的”和“ $ a $是严格的正面”，我们还提供了一些新的证明。我们的证据表明，在这一研究领域，有限的线性操作员摩尔 - 芬罗倒数理论的重要性。
Let $A$ be a bounded linear positive operator on a complex Hilbert space $\mathcal{H}.$ Further, let $\mathcal{B}_A\mathcal{(H)}$ denote the set of all bounded linear operators on $\mathcal{H}$ whose $A$-adjoint exists, and $\mathbb{A}$ signify a diagonal operator matrix with diagonal entries are $A.$ Very recently, several $A$-numerical radius inequalities of $2\times 2 $ operator matrices were established by Feki and Sahoo [arXiv:2006.09312; 2020] and Bhunia {\it et al.} [Linear Multilinear Algebra (2020), DOI: 10.1080/03081087.2020.1781037], assuming the conditions "$\mathcal{N}(A)^\perp$ is invariant under different operators in $\mathcal{B}_A(\mathcal{H})$" and "$A$ is strictly positive", respectively. In this paper, we prove a few new $\mathbb{A}$-numerical radius inequalities for $2\times 2$ and $n\times n$ operator matrices. We also provide some new proofs of the existing results by relaxing different sufficient conditions like "$\mathcal{N}(A)^\perp$ is invariant under different operators" and "$A$ is strictly positive". Our proofs show the importance of the theory of the Moore-Penrose inverse of a bounded linear operator in this field of study.
