Operator norm ≈ Operator norm
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Neural Operator: Learning Maps Between Function Spaces Open
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…
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Slowest local operators in quantum spin chains Open
We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobeniu…
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Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve Open
We consider an infinite planar straight strip perforated by small holes along a curve. In such a domain, we consider a general second-order elliptic operator subject to classical boundary conditions on the holes. Assuming that the perforat…
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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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Time-dependent unbounded Hamiltonian simulation with vector norm scaling Open
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable discreti…
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Perfect commuting-operator strategies for linear system games Open
Linear system games are a generalization of Mermin’s magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional o…
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Moving beyond sub-Gaussianity in high-dimensional statistics: applications in covariance estimation and linear regression Open
Concentration inequalities form an essential toolkit in the study of high-dimensional statistical methods. Most of the relevant statistics literature in this regard is, however, based on the assumptions of sub-Gaussian or sub-exponential r…
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Gabor representations of evolution operators Open
We perform a time-frequency analysis of Fourier multipliers and, more generally, pseudodifferential operators with symbols of Gevrey, analytic and ultra-analytic regularity. As an application we show that Gabor frames, which provide optima…
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Sets of uniformly absolutely continuous norm in symmetric spaces of measurable operators Open
We characterise sets of uniformly absolutely continuous norm in strongly symmetric spaces of -measurable operators. Applications are given to the study of relatively weakly compact and relatively compact sets and to compactness properties …
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Operator Relaxation and the Optimal Depth of Classical Shadows Open
Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli o…
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Refinements of norm and numerical radius inequalities Open
Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if A is a bounded linear operator on a complex Hilbert space, then 14A*A+AA*≤18A+A*…
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Fredholm operators and essential S-spectrum in the quaternionic setting Open
For bounded right linear operators, in a right quaternionic Hilbert space with a left multiplication defined on it, we study the approximate S-point spectrum. In the same Hilbert space, then we study the Fredholm operators and the Fredholm…
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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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Convergence of Special Sequences of Semi-Exponential Operators Open
Several papers, mainly written by J. de la Call and co-authors, contain modifications of classical sequences of positive linear operators to obtain new sequences converging to limits which are not necessarily the identity operator. Such re…
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Norm of the discrete Cesàro operator minus identity Open
The norm of $C-I$ on $\ell^p$, where $C$ is the Cesàro operator, is shown to be $1/(p-1)$ when $1
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Difference of composition operators over the half-plane Open
We study the differences of composition operators acting on weighted Bergman spaces over the upper half-plane. In this setting not all composition operators are bounded and none are compact. The idea of joint pullback measure is used to gi…
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Generalized weighted composition operators from α-Bloch spaces into weighted-type spaces Open
Some criteria for the boundedness, as well as for the compactness, of the generalized weighted composition operator $D^{n}_{\varphi, u}$ from α-Bloch spaces into weighted-type spaces are given. Estimates for the norm and the essential norm…
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Learning neural operators on Riemannian manifolds Open
Learning mappings between functions (operators) defined on complex computational domains is a common theoretical challenge in machine learning. Existing operator learning methods mainly focus on regular computational domains, and have many…
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Functions of self-adjoint operators in ideals of compact operators Open
For self-adjoint operators $A, B$, a bounded operator $J$, and a function\n$f:\\mathbb R\\to\\mathbb C$ we obtain bounds in quasi-normed ideals of compact\noperators for the difference $f(A)J-Jf(B)$ in terms of the operator $AJ-JB$.\nThe f…
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Essential norm of integral operators on Morrey type spaces Open
In this paper, we investigate the essential norm of two classes of integral operators on Morrey type spaces H 2 K .As an application, we characterize the compactness of these operators.
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Reverse Young-type inequalities for matrices and operators Open
We present some reverse Young-type inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with operator means. More precisely, we show that if $A, B\\in {\\mathfrak…
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Inequalities for operator space numerical radius of 2 × 2 block matrices Open
In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space Mn(X), when X is a numerical radius operator space. Moreover, we establish several inequalities for operator space…
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Universal Scalable Robust Solvers from Computational Information Games and fast eigenspace adapted Multiresolution Analysis Open
We show how the discovery of robust scalable numerical solvers for arbitrary bounded linear operators can be automated as a Game Theory problem by reformulating the process of computing with partial information and limited resources as tha…
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Lp estimates for Dirichlet-to-Neumann operator and applications Open
In this article, we consider the time dependent linear elliptic problem with dynamic boundary condition. We recall the corresponding Dirichlet-to-Neumann operator on $\Gamma$ denoted by $-\Lambda_\gamma$. Then we show that when $\gamma=1$ …
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Norm-parallelism and the Davis–Wielandt radius of Hilbert space operators Open
We present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the Birkhoff--James orthogonality for Hilbert space operators. Moreover, we discuss…
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Optimal Shrinkage of Singular Values Open
We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matri…
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Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators Open
In the present paper, we introduce Stancu type modification of Jakimovski-Leviatan-Durrmeyer operators. First, we estimate moments of these operators. Next, we study the problem of simultaneous approximation by these operators. An upper bo…
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Approximation by max-product operators of Kantorovich type Open
We associate to various linear Kantorovich type approximation operators, nonlinear max-product operators for which we obtain quantitative approximation results in the uniform norm, shape preserving properties and localization results.
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OPERATOR ALGEBRAIC APPROACH TO INVERSE AND STABILITY THEOREMS FOR AMENABLE GROUPS Open
We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\\to\\mathcal\nM$ from an countable, discrete, amenable group $G$ into a von Neumann algebra\n$\\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily\ninv…
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Tight Bounds for Sketching the Operator Norm, Schatten Norms, and Subspace Embeddings Open
We consider the following oblivious sketching problem: given $ε\in (0,1/3)$ and $n \geq d/ε^2$, design a distribution $\mathcal{D}$ over $\mathbb{R}^{k \times nd}$ and a function $f: \mathbb{R}^k \times \mathbb{R}^{nd} \rightarrow \mathbb{…