Operator matrix
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Spin-adapted matrix product states and operators Open
Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited i…
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Some improvements of numerical radius inequalities of operators and\n operator matrices Open
We obtain upper bounds for the numerical radius of a product of Hilbert space\noperators which improve on the existing upper bounds. We generalize the\nnumerical radius inequalities of $n\\times n$ operator matrices by using\nnon-negative …
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Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results Open
We present recent analytic results for the 3-loop corrections to the massive operator matrix element $A_{Qg}^{(3)}$for further color factors. These results have been obtained using the method of arbitrarily large moments. We also give an o…
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On inequalities for A-numerical radius of operators Open
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ Inequalities are presented concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recentl…
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Reverse Jensen-Mercer Type Operator Inequalities Open
Let $A$ be a selfadjoint operator on a Hilbert space $\mathcal{H}$ with spectrum in an interval $[a,b]$ and $\phi:B(\mathcal{H})\rightarrow B(\mathcal{K})$ be a unital positive linear map, where $\mathcal{K}$ is also a Hilbert space. Let $…
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Some generalizations of numerical radius on off-diagonal part of 2 × 2 operator matrices Open
We generalize several inequalities involving powers of the numerical radius for offdiagonal part of 2 × 2 operator matrices of the form T = 0 B C 0 , where B,C are two operators.In particular, if
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Improvement of $A$-numerical radius inequalities of semi-Hilbertian\n space operators Open
Let $\\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive\noperator on $\\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of\noperators in semi-Hilbertian space $\\mathcal{B}_A(\\mathcal{H})$ that generalize\na…
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Analysis of the spectrum of a 2x2 operator matrix. Discrete spectrum asymptotics Open
We consider a 2 × 2 operator matrix Aµ, µ > 0 related with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles.We obtain an analog of the Fad…
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On Some Generalizations of Cauchy–Schwarz Inequalities and Their Applications Open
The aim of this paper is to provide new upper bounds of ω(T), which denotes the numerical radius of a bounded operator T on a Hilbert space (H,⟨·,·⟩). We show the Aczél inequality in terms of the operator |T|. Next, we give certain inequal…
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ON RELATIVE ESSENTIAL SPECTRA OF BLOCK OPERATOR MATRICES AND APPLICATION Open
In this paper, we investigate relative essential spectra of $2{\times}2$ block operator matrix using the Fredholm perturbation theory. Furthermore, an example for two-group transport equations is presented to illustrate the validity of the…
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Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results Open
We present recent analytic results for the 3-loop corrections to the massive operator matrix element $A_{Qg}^{(3)}$ for further color factors. These results have been obtained using the method of arbitrarily large moments. We also give an …
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Operator limits of random matrices Open
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are discu…
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On inequalities for A-numerical radius of operators Open
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently i…
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Spectral inclusion for unbounded diagonally dominant $n\times n$ operator matrices Open
In this paper, we establish an analytic enclosure for the spectrum of unbounded linear operators~$\\mathcal{A} $ admitting an $n \\times n$ matrix representation in a Hilbert space $\\mathcal{H} =\\mathcal{H} _1\\oplus \\cdots \\oplus \\ma…
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Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis Open
The spectral analysis of matrix-valued difference equations of second order having polynomial-type Jost solutions, was first used by Aygar and Bairamov.They investigated this problem on semi-axis.The main aim of this paper is to extend sim…
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A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices Open
The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive …
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On the spectrum and Hilbert Schimidt properties of generalized Rhaly matrices Open
In this paper, we show that the multiplications of some generalized Rhaly operators are Hilbert Schimidt operators.We also calculate the spectrum and essential spectrum of a special generalized Rhaly matrices on the Hardy space H².
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Concrete minimal 3 × 3 Hermitian matrices and some general cases Open
Given a Hermitian matrix M ∈ M 3 (ℂ) we describe explicitly the real diagonal matrices D M such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M 3 (ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniqu…
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SOME INEQUALITIES FOR THE NUMERICAL RADIUS FOR HILBERT SPACE OPERATORS Open
We introduce some new refinements of numerical radius inequalities for Hilbert space invertible operators. More precisely, we prove that if $T\in {\mathcal{B}}({\mathcal{H}})$ is an invertible operator, then $\Vert T\Vert \leq \sqrt{2}\uni…
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Spectra of 2×2 upper triangular operator matrices with unbounded entries Open
In this paper, some properties of the spectrum, the approximate point spectrum, the detect spectrum and the essential spectrum of unbounded 2 2 upper triangular operator matrices with diagonal domain in Hilbert space are studied. Moreover,…
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Orthogonality and Numerical radius inequalities of operator matrices Open
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of numeric…
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Some numerical radius inequalities for semi-Hilbert space operators Open
Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$. Let $ω_A(T)$ and ${\|T\|}_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an oper…
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Some refinements of numerical radius inequalities for 2 × 2 operator matrices Open
In this paper, new numerical radius inequalities for 2× 2 operator matrices are proved.These numerical radius inequalities refine the existing upper bounds.
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Positive solutions of the system of operator equations $A_1X=C_1,XA_2=C_2, A_3XA^*_3=C_3, A_4XA^*_4=C_4$ in Hilbert $C^*$-modules Open
Necessary and sufficient conditions are given for the operator system $A_1X=C_1$, $XA_2=C_2$, $A_3XA^*_3=C_3$, and $A_4XA^*_4=C_4$ to have a common positive solution, where $A_i$'s and $C_i$'s are adjointable operators on Hilbert $C^*$-mod…
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Maximal L-regularity and H∞-calculus for block operator matrices and applications Open
Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ABCD] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered,…
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Matrix range characterizations of operator system properties Open
For finite-dimensional operator systems ST, T∈B(H)d, we show that the local lifting property and 1-exactness of ST may be characterized by measurements of the disparity between the matrix range W(T) and the minimal/maximal matrix convex se…
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2×2 operator matrix with real parameter and its spectrum Open
In the present paper we consider a linear bounded self-adjoint 2×2 block operator matrix A μ (so called generalized Friedrichs model) with real parameter μ ∈ R . It is associated with the Hamiltonian of a system consisting of at most two p…
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On the bands of the Schrödinger operator with a matrix potential Open
In this article, we consider the one‐dimensional Schrödinger operator with a Hermitian periodic matrix potential Q . We investigate the bands and gaps of the spectrum and prove that most of the positive real axis is overlapped by m bands. …
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Erratum: Scattering theory for the matrix Schrödinger operator on the half line with general boundary conditions [J. Math. Phys. 56, 092103 (2015)] Open
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Refined inequalities for the numerical radius of Hilbert space operators Open
We present some new upper and lower bounds for the numerical radius of bounded linear operators on a complex Hilbert space and show that these are stronger than the existing ones. In particular, we prove that if $A$ is a bounded linear ope…