THE GEOMETRIC MEANS IN BANACH -ALGEBRAS

THE GEOMETRIC MEANS IN BANACH -ALGEBRAS
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Banach-代数中的几何平均值

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发表时间：
2007
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通讯作者：
B. Feng
B. Feng
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文献类型：
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作者：
B. Feng

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算术-几何-调和不等式在初等数学中占有特殊的地位。在过去的二十五年里(见(1)、（2)、(8)等），许多数学家研究了算术-几何-调和不等式的各种矩阵形式。如何将算术-几何-调和不等式推广到巴拿赫代数中是一个有趣的问题。本文定义了Banach -代数中正元的几何均值，并证明了Banach -代数中存在算术-几何调和不等式。
The arithmetic-geometric-harmonic inequality has played a spe- cial role in elementary mathematics. During the past twenty five years (see (1), (2) and (8) etc.) a great many mathematicians have researched on various kinds of matrix versions of the arithmetic-geometric-harmonic inequality. It is interesting to see whether the arithmetic-geometric-harmonic inequality can be extended to the context of Banach -algebras. In this article we will define the geometric means of positive elements in Banach -algebras and prove that the arithmetic-geometric-harmonic inequality does hold in Banach -algebras.