Norm Inequalities Research Articles

Moving horizon estimation for localization of mobile robots with measurement outliers

This paper investigates the moving horizon estimation (MHE) problem of mobile robots with measurement outliers. To deal with measurement outliers, the Euclidean distance of measurement error is introduced to detect and remove abnormal data. Then, we use dimension expansion methods to preprocess the data of heterogeneous sensors, such as UWB and IMU. An MHE-based method is proposed that deals with the localization of mobile robots with measurement outliers in the presence of bounded noise. An MHE-based estimator is obtained by solving a regularized least-squares problem. We analyze the convergence of the estimation error system using the properties of norm inequalities, and an upper bound is derived for the estimation error system by using norm inequality. Finally, simulation and experiment examples are given to verify the effectiveness and applicability of the proposed approach.

Weighted norm inequalities, embedding theorems and integration operators on vector-valued Fock spaces

Weighted norm inequalities, embedding theorems and integration operators on vector-valued Fock spaces

On Berezin norm and Berezin number inequalities for sum of operators

Abstract The aim of this study is to obtain several inequalities involving the Berezin number and the Berezin norm for various combinations of operators acting on a reproducing kernel Hilbert space. First, we present some bounds regarding the Berezin number associated with W * Q + W * Q ′ {W}^{* }Q+{W}^{* }Q^{\prime} , where W W , Q Q , and Q ′ Q^{\prime} are three bounded linear operators. Next, several Berezin norm and Berezin number inequalities for the sum of n n operators are established.

Further norm inequalities for positive semidefinite matrices

Further norm inequalities for positive semidefinite matrices

Weighted norm inequalities for integral transforms with splitting kernels

We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to satisfy upper bounds given by products of two functions, one in each variable. The obtained results are applicable to a number of transforms, some of which are included here as particular examples. Some of the new results derived here are the characterization of weights for the boundedness of the $\mathscr{H}_\alpha$ (or Struve) transform in the case $\alpha>\frac{1}{2}$, or the characterization of power weights for which the Laplace transform is bounded in the limiting cases $p=1$ or $q=\infty$.

Upper bounds for the norm of the sum and Kronecker product of Hilbert space operators

Upper bounds for the norm of the sum and Kronecker product of Hilbert space operators

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.

Refined Kato inequality and applications to norm and numerical radius inequalities

Refined Kato inequality and applications to norm and numerical radius inequalities

Norm inequalities for functions of matrices

In this paper, we prove several spectral norm and unitarily invariant norm inequalities for matrices in which the special cases of our results present some known inequalities. Also, some of our results give interpolating inequalities which are related to well-known recent inequalities.

A variational proof of a disentanglement theorem for multilinear norm inequalities

The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately. On the one hand, the theorem gives a uniform approach to classical results including Maurey's factorisation theorem and Lozanovskiĭ's factorisation theorem, and, on the other hand, it underpins the duality theory for multilinear norm inequalities developed in our previous two papers.In this paper we give a simple proof of this basic disentanglement theorem. Whereas the approach of our previous paper was rather involved – it relied on the use of minimax theory together with weak*-compactness arguments in the space of finitely additive measures, and an application of the Yosida–Hewitt theory of such measures – the alternate approach of this paper is rather straightforward: it instead depends upon elementary perturbation and compactness arguments.

Bilinear sparse domination for oscillatory integral operators

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to Hörmander symbol classes Sρ,δm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S^m_{\\rho ,\\delta }$$\\end{document} for all 0≤ρ≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le \\rho \\le 1$$\\end{document} and 0≤δ<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le \\delta < 1$$\\end{document}, a notable example is the Schrödinger operator. As a consequence, one obtains weak (1, 1) estimates, vector-valued estimates, and a wide range of weighted norm inequalities for these classes of operators.

Norm inequalities in $${\mathcal {L}}({\mathcal {X}})$$ and a geometric constant

Norm inequalities in $${\mathcal {L}}({\mathcal {X}})$$ and a geometric constant

Norm inequalities for product of matrices

Norm inequalities for product of matrices

A note on Rubio de Francia's extrapolation in tent spaces and applications

The Rubio de Francia extrapolation theorem is a very powerful result which states that in order to show that certain operators satisfy weighted norm inequalities with Muckenhoupt weights it suffices to see that the corresponding inequalities hold for some fixed exponent, for instance p=2. In this paper we extend this result and show that this extrapolation principle allows one to obtain weighted estimates in tent spaces. From our extrapolation result we automatically derive new estimates (and reprove some other) concerning Calderón-Zygmund operators, operators associated with the Kato conjecture, or fractional operators.

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(λ)=∑k=0∞akλk and its modified version ha(λ)=∑k=0∞|ak|λk. The convergence of h(λ) is assumed on the open disk D(0,R), where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities.

Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces

Consider the power series with complex coefficients h(z)=∑k=0∞akzk and its modified version ha(z)=∑k=0∞|ak|zk. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h(z) on the open disk D(0,ρ), where ρ denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.

Singular value and unitarily invariant norm inequalities for matrices

Singular value and unitarily invariant norm inequalities for matrices

Numerical radius and p-Schatten norm inequalities for power series of operators in Hilbert spaces

Let $H$ be a complex Hilbert space. Assume that the power series with complex coefficients $f(z):=\sum\nolimits_{k=0}^{\infty }a_{k}z^{k}$ is convergent on the open disk $D(0,R),~f_{a}(z):=\sum\nolimits_{k=0}^{\infty}\left\vert a_{k}\right\vert z^{k}$ that has the same radius of convergence $R$ and $A,~B,~C\in B(H)$ with $\left\Vert A\right\Vert $ &amp;lt;$R$, then we have the following Schwarz type inequality $ \left\vert \left\langle C^{\ast }Af(A)Bx,y\right\rangle \right\vert \leq f_{a}(\left\Vert A\right\Vert )\left\langle \left\vert \left\vert A\right\vert ^{\alpha }B\right\vert ^{2}x,x\right\rangle ^{1/2}\left\langle \left\vert \left\vert A^{\ast }\right\vert ^{1-\alpha }C\right\vert ^{2}y,y\right\rangle ^{1/2} $ for $\alpha \in \lbrack 0,1]$ and $x,y\in H.$ Some natural applications for numerical radius and p-Schatten norm are also provided.

Simpson Type Tensorial Norm Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities of the form $$\bigg|\bigg|\frac{1}{3}\left(2\operatorname{exp}\left(A\right)\otimes 1-\operatorname{exp}\left(\frac{A\otimes 1 +1\otimes B}{2}\right)+2\cdot 1\otimes \operatorname{exp}\left(B\right)\right)$$ $$-(1\otimes B-A\otimes 1)^{-1}\times\bigg(\operatorname{exp}(1\otimes B)-\operatorname{exp}(A\otimes 1)\bigg)\bigg|\bigg|$$ $$\leqslant \norm{1\otimes B-A\otimes 1}\frac{5}{12}\operatorname{exp}(M)$$ are obtained with variations due to the convexity properties of the mapping $f$.

A Class of Norm Inequalities for Operator Monotone Functions and Hyponormal Operators

A Class of Norm Inequalities for Operator Monotone Functions and Hyponormal Operators