关于Heinz均值的Log-次优化不等式

蒋雪瑶; 韩亚洲

doi:10.13568/j.cnki.651094.651316.2020.06.19.0001

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关于Heinz均值的Log-次优化不等式

更新时间：2026-01-21

- 关于Heinz均值的Log-次优化不等式
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 38, Issue 4, Pages: 397-406(2021)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2020.06.19.0001
  CLC： O178
- Published：2021
- 稿件说明：
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[1]蒋雪瑶,韩亚洲.关于Heinz均值的Log-次优化不等式[J].新疆大学学报(自然科学版)(中英文),2021,38(04):397-406+424.
[1]蒋雪瑶,韩亚洲.关于Heinz均值的Log-次优化不等式[J].新疆大学学报(自然科学版)(中英文),2021,38(04):397-406+424. DOI： 10.13568/j.cnki.651094.651316.2020.06.19.0001.

DOI：10.13568/j.cnki.651094.651316.2020.06.19.0001.

摘要

本文利用广义奇异值的方法给出了与半有限冯·诺依曼代数中算子的Heinz均值相关的log-次优化不等式

将相对应的一些矩阵形式的不等式推广到了算子的情形

并得到了如下结论:Λh(f(x)g(y)+f(y)g(x))≤Λh1/2((f (x)~2+f (y)2)(g(x)~2+g(y)2))

其中0≤x

y∈M

h> 0

f和g都是算子凹函数.同时我们还得到了一些与Heinz均值相关的其它形式的log-次优化不等式.

Abstract

In this paper

the inequality related to Heinz mean in matrix version is extended to operator version

and some logarithmic submajorisation inequalities related to Heinz means of operator on a semi-finite von Neumann algebra M are presented by1 using the technique of generalized singular values. There are mainly Λh( f(x)g(y) + f(y)g(x)) ≤ Λh~2 (( f(x)~2+ f(y)2)(g(x)~2+g(y)2))

where 0 ≤ x

y ∈ M

h > 0

f and g are operator concave functions. In addition

other forms of logarithmic submajorisation inequalities are also generalizalied.

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Keywords

references

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