Refined Heinz operator inequalities

Motivated by the well-known Heinz norm inequalities, in this article we study the corresponding Heinz operator inequalities. We derive the whole series of refinements of these operator inequalities, first with the help of the well-known Hermite–Hadamard inequality, and then, utilizing the parametrized family of the so-called Heron means. In such a way, we obtain improvements of some recent results, known from the literature.     

The converse of the Loewner–Heinz inequality via perspective

The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indeed, we give perspective inequalities equivalent to the Loewner–Heinz inequality.     

On Young and Heinz inequalities for τ-measurable operators

The purpose of this article is to prove Young and Heinz inequalities for τ-measurable operators.     

Improved Young and Heinz inequalities for matrices

We give refinements of the classical Young inequality for positive real numbers and we use these refinements to establish improved Young and Heinz inequalities for matrices.     

Heinz type inequalities for mappings satisfying Poisson’s equation

In this paper, we study the Heinz type inequalities for mappings satisfying Poisson’s equation. Some results generalize the ones obtained by Partyka and Sakan.     

Reverse Young and Heinz inequalities for matrices

We give reverses of the classical Young inequality for positive real numbers and we use these to establish reverse Young and Heinz inequalities for matrices.     

Some matrix inequalities related to Kwong functions

The aim of this note is to investigate some inequalities related to Kwong functions. Refinements of Kaur’s and Zhan’s inequality are presented by the Hadamard product. In addition, variations of the Heinz–Heron type means on Kwong functions are also given.     

Operator-norm inequalities and interpolated trace inequalities

In this article, we investigate some operator-norm inequalities related to some conjectures posed by Hayajneh and Kittaneh that are related to questions of Bourin regarding a special type of inequalities referred to as subadditivity inequalities. While some inequalities are meant to answer these conjectures, other inequalities present reverse-type inequalities for these conjectures. Then, we present some new trace inequalities related to Heinz means inequality and use these inequalities to prove some variants of the aforementioned conjectures.     

矩阵的几个不等式

利用谱分解定理和几个标量不等式,得到了矩阵加权几何均值和酉不变范数的几个不等式,它们是Kittaneh和Manasrah所得相关结果的改进.     

Operator inequalities and reverse inequalities related to the Kittaneh–Manasrah inequalities

This work is concerned with exploring more refinement forms of the Young inequalities and the Kittaneh–Manasrah inequalities. We deduce the Operator version inequalities and reverse version inequalities related to the Kittaneh–Manasrah inequalities.     

An application of Furuta inequality and its best possibility

This paper shows the best possibility for outer exponents of some inequalities under some conditions, and a counter example is obtained.     

Improved Heinz inequalities via the Jensen functional

By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.     

具有负指数的Furuta型不等式的推广

该文首先证明了具有负指数的Furta型不等式等价于Tanahashi的不等式，其次证明了该不等式可以推广为一个保序不等式     

Numerous refinements of Pólya and Heinz operator inequalities

In this article, we present an infinite number of refinements of the Heinz inequality for real numbers and operators. Making use of them, infinitely many refinements of the classical Pólya inequality and their operator versions are deduced.     

THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES

In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.     

Bohr Inequality for Multiple Op erators

An absolute value equation is established for linear combinations of two operators. When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained. Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2] and [3].     

Inequalities of Reid type and Furuta

Two of the most useful inequality formulas for bounded linear operators on a Hilbert space are the Löwner-Heinz and Reid's inequalities. The first inequality was generalized by Furuta (so called the Furuta inequality in the literature). We shall generalize the second one and obtain its related results. It is shown that these two generalized fundamental inequalities are all equivalent to one another.

     

Spectral radius inequalities for Hilbert space operators

We prove several spectral radius inequalities for sums, products, and commutators of Hilbert space operators. Pinching inequalities for the spectral radius are also obtained.