Relation between Two Operator Inequalities img src=quot;http://latex.codecogs.com/gif.latex?f(B^{rac{1}{2}}AB^{rac{1}{2}})geqamp;space;B^{-1}quot;title=quot;f(B^{rac{1}{2}}AB^{rac{1}{2}})geq B^{-1}quot;/and img src=quot;http://latex.codecogs.com/gif.latex?A^{-1}geqamp;space;g(A^{rac{1}{2}}BA^{rac{1}{2}})quot;title=quot;A^{-1}geq g(A^{rac{1}{2}}BA^{rac{1}{2}})quot;/

摘要

We shall show relation between two operator inequalities ?and for positive, invertible operators A and B, where f and g are non-negative continuous invertible functions on satisfying f(t)g(t)=t-1 .