关于正算子的Young不等式

Young's Inequality for Positive Operators

中文关键词:  Young不等式  正算子  泊松积分公式.

英文关键词:Young's inequality  positive operator.

中文摘要:

      本文首先将经典Young不等式及其改进应用于希尔伯特空间上的正算子.其次,本文利用相关正算子的泊松积分公式给出了关于算子$A^\frac1pXB^\frac1q- A^\frac1qYB^\frac1p$酉不变范数的一些新不等式估计,其中$A,\ B,\ X,\ Y\in{\mathcal B}({\mathcal H})$满足$A, B\geqslant 0$且$1

英文摘要:

      The classical Young's inequality and its refinements are applied to positive operators on a Hilbert space at first. Based on the classical Poisson integral formula of relevant operators, some new inequalities on unitarily invariant norm of $A^\frac1pXB^\frac1q-A^\frac1qYB^\frac1p$ are obtained with effective calculation, where $A$, $B$, $X$, $Y\in{\cal B}({\cal H})$ with $A$, $B\geqslant 0$ and $1