GEOMETRIC MEAN AND NORM SCHWARZ INEQUALITY

被引：20

作者：

Ando, Tsuyoshi ^{[1
]}

机构：

[1] Hokkaido Univ, Sapporo, Hokkaido, Japan

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2016年 / 7卷 / 01期

关键词：

geometric mean; norm Schwarz inequality; norm inequality; normal operator;

D O I：

10.1215/20088752-31.58073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Positivity of a 2 x 2 operator matrix [GRAPHICS] >= 0 implies root parallel to A parallel to.parallel to C parallel to >= parallel to B parallel to for operator norm parallel to.parallel to. This can be considered as an operator version of the Schwarz inequality. In this situation, for A, C >= 0, there is a natural notion of geometric mean A#C, for which root parallel to A parallel to.parallel to C parallel to >= parallel to A#C parallel to In this paper, we study under what conditions on A, B, and C or on B alone the norm inequality root parallel to A parallel to.parallel to C parallel to >= parallel to B parallel to can be improved as parallel to A#C parallel to >=parallel to B parallel to.

引用

页码：1 / 8

页数：8

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