On refined Young inequalities and reverse inequalities
arXiv:1001.0535
Abstract
In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two different reverse inequalities for the refined Young inequality for two positive operators.
The arised problem in Remark 4.2 in the previous manuscript was partially solved by finding a counter-example. Thus 5 lines from the below in page 8 were deleted