相关论文: Jensen's operator inequality and its converses

We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…

In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.

This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…

We consider the Jacobi operator $(Jf)_n= a_{n-1}f_{n-1}+a_nf_{n+1}+b_nf_n$ on $\Z$ with a real compactly supported sequences $(a_n-1)_{n\in\Z}$ and $(b_n)_{n\in\Z}$. We give the solution of two inverse problems (including characterization):…

We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.

Some inequalities for different types of convexity are established.

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

Let $I$ and $J$ be two intervals, and let $f, g: I \rightarrow \mathbb{R}$. If for any points $a$ and $b$ in $I$ and any positive numbers $p$ and $q$ such that $p + q = 1$, we have \begin{align} \nonumber p f(a) + q f(b) + g(pa + qb) \in J,…

In this article we prove new inequalities for the generalized and the joint spectral radius of bounded sets of positive operators on Banach function and sequence spaces, in particular some inequalities for positive kernel operators that…

In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…

In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…

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…

In this paper, we improve and generalize the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space. Our results are more extensive and precise than many previous results due to Fu and He…

We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…

In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a…

The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space are detected. The existence of extremal functions in the relevant inequalities is also established. Our results…

The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean,…