شماره ركورد كنفرانس :
4079
عنوان مقاله :
Refinements of Young and Heinz inequalities for operators using Kantorovich constant
پديدآورندگان :
Nasiri L. leilanasiri468@gmail.com Lorestan University , Shakoori M. mahmoodshakoori@gmail.com Lorestan University , Sababheh M. Jordan, sababheh@psut.edu.jo Dept. of Basic Science Princess Sumaya Univ. Amman
كليدواژه :
Reverse Young inequality , Hilbert , Schmidt norm , Invertible positive operators , Kantorovich constant , Heinz operator inequality
عنوان كنفرانس :
چهل و هفتمين كنفرانس رياضي ايران
چكيده فارسي :
In this note, we first give some reverse of Young
inequalities. Then we establish operator and matrix inequalities corresponding these inequalities
For example, let $A,B\in B(H)^{++},$ then for $0 \leq \nu \leq \frac{1}{2}$
$$ (1-\nu)^{2\nu } (A \nabla B) +(1-\nu)^{2-2\nu}
H_{2\nu}(A,B)
K(h,2)^{-r} \geq 2 (1-\nu) (A \sharp B)
$$
and
$$ (1-\nu)^{2\nu } H_{2\nu}(A,B)
+(1-\nu)^{2-2\nu} (A \nabla B) K(h,2)^{-r} \geq 2 (1-\nu) (A \sharp B),
$$
where, $h=\frac{b}{a}$ and $r=min\{2 \nu,1-2\nu\}.$
