On reversing of the modified Young inequality

Abstract

Abstract. In the present paper, by Haagerup theorem, we show that if A ∈ M n is a non scalar strictly positive matrix and 0 < ν < 1 be a real number such that ν = 1 2 , then there exists X ∈ M n such that

Matrix inequalities for the difference between arithmetic mean and harmonic mean

“…, and the authors of [13] pointed out that if A and B are positive semidefinite and X ∈ M n (C), then for unitarily invariant norm |A v XB 1−v | ≤ |vAX + (1 − v)XB | does not holds in general.…”

“…F , and the authors of [13] pointed out that if A and B are positive semidefinite and X ∈ M n (C), then for unitarily invariant norm…”

New estimations for the Berezin number inequality

“…A matrix Young inequality was obtained by Ando in [1]. The matrix mean inequality and the matrix Young inequality were considered with the numerical radius norm by Salemi and Sheikhhosseini in [19,20].…”

Advanced refinements of Young and Heinz inequalities

“…Even though this inequality looks very simple, it is of great interest in operator theory. We refer the reader to [5,6,7,8,9,11,15] as a sample of the extensive use of this inequality in this field. Refining this inequality has taken the attention of many researchers in the field, where adding a positive term to the left side is possible.…”