Some refinements of Young type inequality for positive linear map

Rok, strany: 2019, 919 - 930

We obtain a refined Young type inequality in this paper. The conclusion is presented as follows: Let $A, B\in B(\mathcal{H})$ be two positive operators and $p\in[0,1]$, then

$$ A\sharp_p B+G^*(A\sharp_p B)G≤ A\nabla_p B-2r(A\nabla B-A\sharp B), $$

where $r=\min\{p,1-p \} $, $G=\frac{\sqrt{L(2p)}}{2}A^-1S(A|B)$, $L(t)$ is periodic with period one and $L(t)=((t²) / (2))( ((1-t) / (t)) )^2t$ for $t\in[0,1]$. Moreover, we give the $s$-th powering of two inequalities related to the above one with $s>0$ which refines Lin's work. In the mean time, we present an inequality involving Hilbert-Schmidt norm.

ISO 690:

Yang, C., Gao, Y., Lu, F. 2019. Some refinements of Young type inequality for positive linear map. In Mathematica Slovaca, vol. 69, no.4, pp. 919-930. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0277

APA:

Yang, C., Gao, Y., Lu, F. (2019). Some refinements of Young type inequality for positive linear map. Mathematica Slovaca, 69(4), 919-930. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0277

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava