POSITIVITY OF OPERATOR-MATRICES OF HUA-TYPE
POSITIVITY OF OPERATOR-MATRICES OF HUA-TYPE
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DOI：
10.15352/bjma/1240336286
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发表时间：
2008
影响因子：
1.2
通讯作者：
T. Andô
中科院分区：
文献类型：
--
作者：
T. Andô
设Aj（j = 1，2，.，n）是Hilbert空间上的严格压缩。本文研究一个n阶算子矩阵：Hn（A1，A2，…，An）=（（IAjAi）1）n=1。对于n = 2的情形，华（Inequalities involving determinants，Acta Math. Sinica，5（1955），463-470）证明了正性，即，H2（A1，A2）的半正定性。然而，对于n = 3，情况并非总是如此。首先，我们推广了一个已知的条件，保证积极的Hn。我们的主要结果是Hn的正性在严格压缩的开单位圆盘D的算子Mobius映射下保持不变。
Let Aj (j = 1,2,...,n) be strict contractions on a Hilbert space. We study an n ◊ n operator-matrix: Hn(A1,A2,...,An) = ((I A jAi) 1 ) n=1. For the case n = 2, Hua (Inequalities involving determinants, Acta Math. Sinica, 5 (1955), 463-470 (in Chinese)) proved positivity, i.e., positive semi- definiteness of H2(A1,A2). This is, however, not always true for n = 3. First we generalize a known condition which guarantees positivity of Hn. Our main result is that positivity of Hn is preserved under the operator Mobius map of the open unit disc D of strict contractions.