Related papers: Commutator inequalities via Schur products

We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces $\{X(m,n)\}_{m,n=0}^\infty$ equipped…

In the setting of homogeneous spaces (X,d,{\mu}), it is shown that the commutator of Calder\'on- Zygmund type operators as well as commutator of potential operator with BMO function are bounded in generalized Grand Morrey space. Interior…

In this paper we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement-invariant function spaces from analogous…

We prove lower bounds for the worst case error of quadrature formulas that use given sample points $\X_n = \{ x_1, \dots , x_n \}$. We are mainly interested in optimal point sets $\X_n$, but also prove lower bounds that hold with high…

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the…

Several unitarily invariant norm inequalities and numerical radius inequalities for Hilbert space operators are studied. We investigate some necessary and sufficient conditions for the parallelism of two bounded operators. For a finite rank…

We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional…

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…

Let $A$ and $B$ be two densely defined unbounded closeable operators in a Hilbert space such that their unbounded operator products $AB$ and $BA$ are also densely defined. Then all four operators possess adjoints and we obtain new inclusion…

In this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight…

Let $H$ be a complex separable Hilbert space and $B(H)$ the algebra of all bounded linear operators on $H$. In this paper, we give considerable generalizations of the inequalities for norms of commutators of normal operators. Let $S, T \in…

Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…

The aim of this paper is to get the boundedness of the commutators of multi-sublinear operators generated by local campanato functions and multilinear Calder\'on-Zygmund operators on the product generalized local Morrey spaces.

In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.

For a finite, positive, Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$, related to the classical Hausdorff matrix defined by the same measure $\mu$, in the same algebraic way that the Hilbert matrix is related to…

Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space. These inequalities lead to universal bounds on spectral gaps and on moments of eigenvalues lambda_k that are analogous to those known for Schroedinger…

In this paper, we give the Alzer inequality for Hilbert space operators as follows: Let $A, B$ be two selfadjoint operators on a Hilbert space $\mathcal H$ such that $0 < A, B \le \frac{1}{2}I$, where $I$ is identity operator on $\mathcal…

We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by…

In this work, a pre-Gr\"{u}ss inequality for positive Hilbert space operators is proved. So that, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound…