Some new results for Hua-type operator matrices☆
Some new results for Hua-type operator matrices☆
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DOI：
10.1016/j.laa.2016.05.022
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发表时间：
2016-10
影响因子：
1.1
通讯作者：
Yuan Li;Mei-juan Zheng;Shasha Hu
中科院分区：
文献类型：
--
作者：
Yuan Li;Mei-juan Zheng;Shasha Hu
设Ai（i= 1，2，…，n）是Hilbert空间H上的严格压缩映射. n× n算子矩阵H n（A 1，A 2，，An）=（（I-A j A i）-1）i，j= 1 n称为华型算子矩阵。本文主要研究与华型算子矩阵有关的一些结果。首先给出了n× n算子矩阵（I-Aj <$Ai）i，j= 1 n为正的几个等价条件.然后给出方程min {< 1，< 1}= 2.特别地，得到了严格压缩映射A1和A2满足<$H2（A1，A2）<$= 2的等价条件.
Abstract Let A i (i= 1, 2,…, n) be strict contractions on a Hilbert space H. The n× n operator matrix H n (A 1, A 2,⋯, 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 operator matrices (I− A j⁎ A i) i, j= 1 n. Then the equation min {‖ H 2 (A 1, A 2)‖:‖ A 1‖< 1,‖ A 2‖< 1}= 2 is shown. In particular, some equivalent conditions for strict contractions A 1 and A 2 such that‖ H 2 (A 1, A 2)‖= 2 are obtained.