The classical Bohr inequality says that |a+b| ≤ p|a|+q|b| for all scalars a, b and p, q > 0 with 1 p + 1 q = 1. The equality holds if and only if (p− 1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogr...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

Abstract— The direct part of Stein’s lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein’s lemma without using Hiai-Petz’s theorem, along with an operator monotone function, and in addition it is also used to show a new proof of Hiai-Pet...

In the literature of poverty, it is well known that every poverty index should be sensitive to the incidence of poverty, the intensity of poverty and to the inequality among the poo individuals. However, the inequality among the poor could be measured analyzing either the income of the poor distribution, or the gap of the poor distribution. Depending on the side we focus on, contradictory resul...

For a hyponormal operator, C. R. Putnam’s inequality gives an upper bound on the norm of its self-commutator. In the special case of a Toeplitz operator with analytic symbol in the Smirnov space of a domain, there is also a geometric lower bound shown by D. Khavinson (1985) that when combined with Putnam’s inequality implies the classical isoperimetric inequality. For a nontrivial domain, we co...

Trapezoid inequality estimates the difference of integral mean a function on finite interval [a, b] and arithmetic its values at endpoints b. Quantum calculus is based diference principle or without concept limits. Euler-Jackson q-difference operator q-integral are discretization ordinary derivatives integrals they can be generalized to shifted versions arbitrary domain b]. In this paper we dis...