Norm Inequalities For Operators Research Articles

On some operator norm inequalities

In this paper, we use known classical inequalities to establish some operator norm inequalities for a pair of norm-attainable operators on a complex Hilbert space.

Two-weight norm inequalities for rough fractional integral operators on Morrey spaces

We establish the two-weight norm inequalities for the rough fractional integral operators on Morrey spaces.

The norm of the Cesàro operator minus the identity and related operators acting on decreasing sequences

Recently, several authors have considered the problem of determining optimal norm inequalities for discrete Hardy-type operators (like Cesàro or Copson). In this work, we obtain sharp bounds for the norms of the difference of the Cesàro operator with either the identity or the shift, when they are restricted to the cone of decreasing sequences in ℓp (which is closely related to the previously mentioned estimates). Finally, we also address the case of weighted inequalities and find an interesting contrast between the norms of these two difference operators.

New weighted norm inequalities for multilinear singular integral operators with generalized kernels and their commutators

New weighted norm inequalities for multilinear singular integral operators with generalized kernels and their commutators

Weighted norm inequalities for multilinearfractional integral operators on metric measure spaces

Let $({\mathcal~X},~d,~\mu)$ be a metric measurespace satisfying the geometrically doubling condition. We establish some weak type weighted norm inequalitiesfor the multilinear fractional integral operatorand the multilinear fractional maximal function.As an application, we also establish a weak type weighted norm inequalityon Morrey spaces for the multilinear fractional integral.

Norm and numerical radius inequalities for Hilbert space operators

Norm and numerical radius inequalities for Hilbert space operators

On weighted norm inequalities for oscillatory integral operators

We prove weighted norm inequalities with Muckenhoupt’s A_p-weights, for a wide class of oscillatory integral operators. As a consequence, one also obtains the boundedness of commutators of the aforementioned operators with functions in BMO.

Tighter uncertainty relations based on modified weighted Wigner–Yanase–Dyson skew information of quantum channels

We use a novel formation to illustrate the () modified weighted Wigner–Yanase–Dyson (() MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore the sum uncertainty relations for arbitrary N quantum channels and for unitary channels. These uncertainty inequalities are shown to be tighter than the existing ones by a detailed example. Our results are also applicable to the MWWYD skew information and the () modified weighted Wigner–Yanase–Dyson (() MWWYD) skew information of quantum channels as special cases.

Norm Equalities and Inequalities for Operator Matrices

The aim of this thesis is to study some Norm equalities and Inequalities for operator Matrices and some of their properties. Also, we present the aim of this thesis to present some famous norm inequalities for Hilbert space operators which have been studied in literature and some new results.

Perturbation norm inequalities for elementary operators generated by analytic functions with positive Taylor coefficients

Perturbation norm inequalities for elementary operators generated by analytic functions with positive Taylor coefficients

Cauchy–Schwarz norm inequalities for elementary operators and inner product type transformers generated by families of subnormal operators

Cauchy–Schwarz norm inequalities for elementary operators and inner product type transformers generated by families of subnormal operators

Buzano, Kreĭn and Cauchy-Schwarz inequalities

The Cauchy-Schwarz, Buzano and Kre\u{\i}n inequalities are three inequalities about inner product. The main goal of this article is to present refinements of Buzano and Cauchy-Schwarz inequalities, and to present a new proof of a refined version of a Kre\u{\i}n-type inequality. Applications that include Buzano-type inequalities for certain operators, operator norm and numerical radius inequalities of Hilbert space operators will be presented.

FURTHER INEQUALITIES FOR THE EUCLIDEAN OPERATOR RADIUS

By use of some non-negative Hermitian forms defined for n-tuple of bounded linear operators on the Hilbert space (H, h·, ·i) we establish new numerical radius and operator norm inequalities for sum of products of operators

Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions — Corrigendum

Weighted norm inequalities for positive operators restricted on the cone of <i>λ</i>-quasiconcave functions — Corrigendum

Refined Heinz operator inequalities and norm inequalities

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 $A , B, X\in M_n(\mathbb{C})$ such that $A$ and $B$ are positive definite and $f$ is an operator monotone function on $(0,\infty)$. Then \begin{equation*} |||f(A)X-Xf(B)|||\leq \max\{||f'(A)||, ||f'(B)||\} |||AX-XB|||. \end{equation*} Finally we obtain a series of refinements of the Heinz operator inequalities, which were proved by Kittaneh and Krnic.

Two-weight norm inequalities for product fractional integral operators

In the open range 1<p<q<∞, under a certain geometrical condition on weights, two-weight norm inequality for the product fractional integral operator, whose kernel has singularity appeared on each of the coordinate subspaces, is shown to follow from the Fefferman–Phong-type characteristic for the product cubes. This geometrical condition turns out to be the testing condition of Carleson-type embedding for product dyadic cubes.

Some Improvements of the Cauchy-Schwarz Inequality Using the Tapia Semi-Inner-Product

The aim of this article is to establish several estimates of the triangle inequality in a normed space over the field of real numbers. We obtain some improvements of the Cauchy–Schwarz inequality, which is improved by using the Tapia semi-inner-product. Finally, we obtain some new inequalities for the numerical radius and norm inequalities for Hilbert space operators.

Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces

We prove the norm inequalities for potential operators and fractional integrals related to generalized shift operator defined on spaces of homogeneous type. We show that these operators are bounded from $H^{p}_{\Delta_{\nu}}$ to $H^{q}_{\Delta_{\nu}}$, for $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{Q}$, provided $0&amp;lt;\alpha&amp;lt;\frac{1}{2}$, and $\alpha&amp;lt;\beta\leq 1$ and $\frac{Q}{Q+\beta}&amp;lt;p\leq\frac{Q}{Q+\alpha}$. By applying atomic-molecular decomposition of $H^{p}_{\Delta_{\nu}}$ Hardy space, we obtain the boundedness of homogeneous fractional type integrals which extends the Stein-Weiss and Taibleson-Weiss's results for the boundedness of the $B_n$-Riesz potential operator on $H^{p}_{\Delta_{\nu}}$ Hardy space.

Norm and numerical radius inequalities for Hilbert space operators

ABSTRACT We give several norm and numerical radius inequalities for Hilbert space operators. These inequalities improve on some earlier related inequalities. As an application of one of our results, we give a necessary condition for the equality case in the triangle inequality for the usual operator norm.

Two-Weight, Weak-Type Norm Inequalities for a Class of Sublinear Operators on Weighted Morrey and Amalgam Spaces

Let Tα0≤α&lt;n be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let b,Tα0≤α&lt;n be the commutators generated by BMORn functions and Tα. This paper is concerned with two-weight, weak-type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criteria for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces.