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About 8,349 papers for “Operator norm”

Operator Norm Attainment

‎Arpita Mal, Kallol Paul, ‎Debmalya Sain · Infosys science foundation series · 2024

Cited by 0

Operator norm inequalities

Peter Elliott · Cambridge University Press eBooks · 1997

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Cited by 0

On some operator norm inequalities

J. O. Bonyo, Joshua Were · Annals of Mathematics and Computer Science · 2024

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.

Cited by 0Open access

$$\mu$$-Norm of an Operator

Dmitrii Valer'evich Treschev · Proceedings of the Steklov Institute of Mathematics · 2020

Let $$(\mathcal X,\mu)$$ be a measure space. For any measurable set $$Y\subset\mathcal X$$ let $$\mathbf 1_Y: \mathcal X\to{\mathbb R}$$ be the indicator of $$Y$$ and let $$\pi_Y^{}$$ be the orthogonal projection $$L^2(\mathcal X)\ni f\mapsto{\pi_Y^{}}_{} f = \mathbf 1_Y f$$ . For any bounded operator $$W$$ on $$L^2(\mathcal X,\mu)$$ we define its $$\mu$$ -norm $$\|W\|_\mu = \inf_\chi\sqrt{\sum\mu(Y_j)\|W\pi_Y^{}\|^2}$$ , where the infimum is taken over all measurable partitions $$\chi=\{Y_1,\dots,Y_J\}$$ of $$\mathcal X$$ . We present some properties of the $$\mu$$ -norm and some computations. Our main motivation is the problem of constructing a quantum entropy.

Cited by 5Open access

Metric sparsification and operator norm localization

Xiaoman Chen, Romain Tessera, Xianjin Wang et al. · ArXiv.org · 2007

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists a positive number c such that for every r>0, there is R>0 for which, if m is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded linear operator acting on L^2(X,m) with propagation r, then there exists an unit vector v satisfying with support of diameter at most R and such that |Tv| is larger or equal than c|T|. If X has finite asymptotic dimension, then X has operator norm localization property. In this paper, we introduce a sufficient geometric condition for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that any sequence of expanding graphs does not possess the operator norm localization property.

Cited by 1Open access

On the Norm of Elementary Operator

Denis Njue Kingangi, J. O. Agure, Fredrick Oluoch Nyamwala · Advances in Pure Mathematics · 2014

The norm of an elementary operator has been studied by many mathematicians. Varied results have been established especially on the lower bound of this norm. Here, we attempt the same problem for finite dimensional operators.

Cited by 6Open access

The norm of a circulant operator

Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric · R-libre (Université Téluq) · 2022

In this talk, we’ll present our study of the induced p-norm of circulant matrices A(n, +/- a, b), acting as operators on the Euclidean space R^n. For circulant matrices whose entries are nonnegative real numbers, in particular for A(n, a, b), we provide an explicit formula for the p-norm, p greater than one. The calculation for A(n, −a, b) is more complex. The 2-norm is precisely determined. As for the other values of p, two different categories of upper and lower bounds are obtained. These bounds are optimal at the end points (i.e. p = 1 and p = infinity) as well as at p = 2.

Cited by 0

Numerical Radius and Operator Norm Inequalities

Khalid Shebrawi, Hussien Albadawi · Journal of Inequalities and Applications · 2009

A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if A and B are operators on a complex Hilbert space H, then wr(A∗B)≤(1/2)‖|A|2r+|B|2r‖ for r≥1. It is also shown that if Xi is normal (i=1,2,…,n), then ‖∑i=1nXi‖r≤nr−1‖∑i=1n|Xi|r‖. Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented.

Cited by 42Open access

OPERATOR NORM INEQUALITIES OF MINKOWSKI TYPE

Khalid Shebrawi, Hussien Albadawi · 2008

ABSTRACT. Operator norm inequalities of Minkowski type are presented for unitarily invariant norm. Some of these inequalities generalize an earlier work of Hiai and Zhan.

Cited by 29

Numerical Radius and Operator Norm Inequalities

Khalid Shebrawi, Hussien Albadawi · Greater South Information System · 2009

A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if and are operators on a complex Hilbert space , then for . It is also shown that if is normal , then . Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented.

Cited by 0Open access