当前位置: X-MOL 学术Ann. Funct. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the weighted geometric mean of accretive matrices
Annals of Functional Analysis ( IF 1.2 ) Pub Date : 2020-10-07 , DOI: 10.1007/s43034-020-00094-6
Yassine Bedrani , Fuad Kittaneh , Mohammed Sababheh

In this paper, we discuss new inequalities for accretive matrices through non-standard domains. In particular, we present several relations for $$A^r$$ and $$A\sharp _rB$$ , when A, B are accretive and $$r\in (-1,0)\cup (1,2).$$ This complements the well-established discussion of such quantities for accretive matrices when $$r\in [0,1],$$ and provides accretive versions of known results for positive matrices. Among many other results, we show that the accretive matrices A, B satisfy $$\begin{aligned} \mathfrak {R}(A\sharp _rB)\le \mathfrak {R}A\sharp _r \mathfrak {R}B, r\in (-1,0)\cup (1,2). \end{aligned}$$ This, and other results, gain their significance due to the fact that they are reversed when $$r\in (0,1).$$

中文翻译:

关于增生矩阵的加权几何平均

在本文中,我们通过非标准域讨论了增积矩阵的新不等式。特别地,我们给出了 $$A^r$$ 和 $$A\sharp _rB$$ 的几个关系,当 A, B 是增生的并且 $$r\in (-1,0)\cup (1,2) .$$ 当 $$r\in [0,1],$$ 时,这补充了对增加矩阵的此类数量的完善讨论,并提供了正矩阵已知结果的增加版本。在许多其他结果中,我们表明增生矩阵 A、B 满足 $$\begin{aligned} \mathfrak {R}(A\sharp _rB)\le \mathfrak {R}A\sharp _r \mathfrak {R}B , r\in (-1,0)\cup (1,2)。\end{aligned}$$ 这个结果和其他结果之所以重要,是因为当 $$r\in (0,1).$$
更新日期:2020-10-07
down
wechat
bug