相关论文: Reverses of operator Acz\'el inequality
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…
In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…
We present several Ando-Hiai type inequalities for $n$-variable operator means for positive invertible operators. Ando-Hiai's inequalities given here are not only of the original type but also of the complementary type and of the reverse…
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown,…
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed…
We give a Jensen operator inequality for strongly convex functions. As a corollary, we improve operator Holder-McCarthy inequality under suitable conditions.
In this note, some refinements of Young inequality and its reverse for positive numbers are proved and using these inequalities some operator versions and Hilbert-Schmidt norm versions for matrices of these inequalities are obtained.
Inequalities for the transformation operator kernel $A(x,y)$ in terms of $F$-function are given, and vice versa. These inequalities are applied to inverse scattering on half-line. Characterization of the scattering data corresponding to the…
We present several sharp upper bounds and some extension for product operators. Among other inequalities, it is shown that if , , are non-negative continuous functions on such that , , then for all non-negative operator monotone decreasing…
Let $\mu_p(A,B,t)=(tA^p+(1-t)B^p)^{1/p}$ denote the weighted power mean between positive operators $A$ and $B$. We show that the function $t\to \|A-\mu_p(A,B,t)\|_2$ is monotonically decreasing whenever $1/2 \leq p \leq 1$. Hence showing…
We start to investigate how small changes on the definition of ordinary means affect their properties. Especially the property of being a mean. In that direction we are looking for weakenings of the basic defining property of means. Hence…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
We present ten different characterizations of functions satisfying a weak reverse H\"older inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak…
Generalization of functions of bounded mean oscillation and Hankel operators to the case of compact abelian groups with linearly ordered dual is considered. Spaces of functions of bounded mean oscillation and of bounded mean oscillation of…
The original Ando-Hiai and Golden-Thompson inequalities present comparisons for the operator geometric mean $\sharp_v$ when $0\leq v\leq 1.$ Our main target in this article is to study these celebrated inequalities for means other than the…
In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…
An integral representation of an operator mean via the power means is obtained. As an application, we shall give explicit condition of operator means that the Ando-Hiai inequality holds.