2020/09/06 by Ghazanfari, Amir Ghasem
#15A45 #47A30 #47A63 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2009.02666
In this article we study the Heinz and Hermite-Hadamard inequalities. We derive the whole series of refinements of these inequalities involving unitarily invariant norms, which improve some recent results, known from the literature. We also prove that if A , B, X∈ Mn(ℂ) such that A and B are positive definite and f is an operator monotone function on (0,∞). Then |||f(A)X-Xf(B)|||≤ max\||f'(A)||, ||f'(B)||\ |||AX-XB|||. Finally we obtain a series of refinements of the Heinz operator inequalities, which were proved by Kittaneh and Krnić.