The upper bound of a reserve Hölder's type operator inequality and its applications

Abstract

In our previous paper, we obtained a reverse Hölder's type inequality which gives an upper bound of the difference: with a parameter , for -tuples and of positive numbers and for , satisfying . In this paper for commutative positive operators and on a Hilbert space and a unit vector , we give an upper bound of the difference As applications, considering special cases, we induce some difference and ratio operator inequalities. Finally, using the geometric mean in the Kubo-Ando theory we shall give a reverse Hölder's type operator inequality for noncommutative operators.

Keywords

• Hölder's inequality
• Difference inequality
• Ratio inequality
• Reverse Hölder's inequality
• Geometric mean