Some new results for Hua-type operator matrices

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• 作者：Yuan Li ; ^{liyuan0401@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Mei Zheng ; Shasha Hu
• 关键词：47A30 ; 47B65 ; 47B15
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：506
• 期：Complete
• 页码：212-225
• 全文大小：293 K

文摘

Let hURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516301847&_mathId=si1.gif&_user=111111111&_pii=S0024379516301847&_rdoc=1&_issn=00243795&md5=9f566079dbc8214b66012be5973fd28d">$A_i(i=1,2,\dots ,n)$ be strict contractions on a Hilbert space H$\mathcal{H}$. The n×n$n\times n$ operator matrix $H_n(A_1,A_2,\cdots ,A_n)={({(I-A_j^{⁎}{A}_i)}^{-1})}_{i,j=1}^n$ is called a Hua-type operator matrix. In this note, we mainly investigate some results which are related to the Hua-type operator matrix. We firstly give some equivalent conditions for the positivity of n×n$n\times n$ operator matrices ${(I-A_j^{⁎}{A}_i)}_{i,j=1}^n$. Then the equation min{‖H₂(A₁,A₂)‖:‖A₁‖<1,‖A₂‖<1}=2$\mathit{min}\{\Vert H_2(A_1,A_2)\Vert :\Vert A_1\Vert <1,\Vert A_2\Vert <1\}=2$ is shown. In particular, some equivalent conditions for strict contractions A₁$A_1$ and A₂$A_2$ such that ‖H₂(A₁,A₂)‖=2$\Vert H_2(A_1,A_2)\Vert =2$ are obtained.