有关算子的一些Log-次优化不等式和对称拟范数不等式

王云; 闫成

doi:10.13568/j.cnki.651094.651316.2020.06.06.0002

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有关算子的一些Log-次优化不等式和对称拟范数不等式

更新时间：2026-01-21

- 有关算子的一些Log-次优化不等式和对称拟范数不等式
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 38, Issue 4, Pages: 407-424(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.651094.651316.2020.06.06.0002
  CLC： O177
- Published：2021
- 稿件说明：
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[1]王云,闫成.有关算子的一些Log-次优化不等式和对称拟范数不等式[J].新疆大学学报(自然科学版)(中英文),2021,38(04):407-424.
[1]王云,闫成.有关算子的一些Log-次优化不等式和对称拟范数不等式[J].新疆大学学报(自然科学版)(中英文),2021,38(04):407-424. DOI： 10.13568/j.cnki.651094.651316.2020.06.06.0002.

DOI：10.13568/j.cnki.651094.651316.2020.06.06.0002.

摘要

本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间

xi∈E(M)~((p)+)

yi∈E(M)~((p)+)使得x_iyi=y_ixi

i=1

…

我们证明了‖(∑j=1~kxi1/2yi1/2)2‖_(E(M)~((r)))≤‖(∑j=1~kxi)1/2(∑j=1~kyi)(∑j=1~kxi)1/2‖_(E(M)~((r)))≤‖(∑j=1~kxi)(∑j=1~kyi)‖_(E(M)~((r)))其中1≤p

Abstract

Using the method of majorization and the properties of quasi-norms

we give some quasi-norm inequalities related to Hayajneh and Kittaneh's conjecture for operator in semifinite von Neumann algebras.Let E(M) be symmetric quasi-Banach space and let xi∈E(M)~((p)+)

yi∈E(M)~((p)+) with y_ixi=y_ixi

i=1

…

then‖(∑j=1~kxi1/2yi1/2)2‖_(E(M)~((r)))≤‖(∑j=1~kxi)1/2(∑j=1~kyi)(∑j=1~kxi)1/2‖_(E(M)~((r)))≤‖(∑j=1~kxi)(∑j=1~kyi)‖_(E(M)~((r))) Some logarithmic submajorization inequalities for operator in semifinite von Neumann algebras are also considered.

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references

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