Multiple fidelities and joint numerical range

Large language models as experimental systems in human psychopathology: a modelling study.

Although the numerical radius is not sub-multiplicative, we tickle this problem by showing a weak sub-multiplicativity behaviour. This will be discussed for the usual numerical radius, and the recently defined generalized numerical radius for any unitarily invariant norm, defined on an ideal in the C ∗ − algebra of bounded linear operators on a complex Hilbert space.

Abstract We study linear convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the linear dynamics, we indeed identify that convective stability of superposed waves occurs for fewer propagation speeds than for the corresponding single waves. It reflects the interaction that monostable waves have over long distances. Our method relies on numerical range estimates, that imply time-uniform resolvent bounds.

Let A and B be two positive bounded linear operators acting on two complex Hilbert spaces H and K , respectively. In this paper, we study the ( A ⊗ B ) - maximal numerical range W max A ⊗ B ( T ⊗ S ) of the tensor product T ⊗ S for two bounded linear operators T and S on H and K , respectively. In the context of this work, we show under some hyponormality conditions, the following equality W max A ⊗ B ( T ⊗ S ) = co ( W max A ( T ) ⋅ W max B ( S ) ) holds, where W max A ( T ) , W max B ( S ) and co ( ⋅ ) denote respectively the A-maximal numerical range of T, the B-maximal numerical range of S and convex hull. Furthermore, we extend Fong's result to the class of operators defined on the semi-Hilbertian space.

Minimizing numerical radius of weighted cyclic matrices under permutation of the weights

Estimating reaction rate constants from impedance spectra: Simulating the multistep oxygen evolution reaction

Phase-dependent nutrient requirements of broiler breeder hens for day-old chick production in a field study using interpretable machine learning.

We investigate the space of bounded linear operators on a Banach space equipped with a norm which is equivalent to the operator norm such that the subspace of compact operators is an M-ideal. In particular, we show that the space of compact operators on ℓ p ( 1 < p < ∞ ) equipped with the numerical radius norm is an M-ideal whenever the numerical index of ℓ p is not 0 (for all values of p in the complex case, for p ≠ 2 in the real case). On the other hand, we show that the space of compact operators on a Banach space containing an isomorphic copy of ℓ 1 whose numerical index is greater than 1/2 is not an M-ideal. We also study the proximinality, the existence of farthest points and the compact perturbation property for the numerical radius.

We establish several numerical radius inequalities for bounded linear operators and the product of operators through Orlicz functions. Many inequalities are consequences of using specific Orlicz functions. In particular, it is shown that for every positive integer n > 1.

In this paper, we obtain some upper bounds for numerical radius of operators which generalize some well-known inequalities for classical numerical radius and refine some recent inequalities concerning the numerical radius inequalities of Hilbert space operators.

Numerical radius and ℓ operator norm of Kronecker products and Schur powers: inequalities and equalities

On numerical range of generalized Aluthge transforms, and a generalization of the arithmetic-geometric mean inequality

Abstract Let A be a positive bounded linear operator acting on a complex Hilbert space H $\mathcal{H}$ . Our aim in this paper is to establish useful properties related to the A -numerical range and A -spectrum of A -bounded operators. In addition, we prove Anderson’s theorem for certain classes of semi-Hilbertian operators. Illustrative examples are also given.

Numerical radius and Euclidean operator radius inequalities on $$C^*$$-algebras

In this paper we investigate the numerical range of 3×3 matrices over finite fields, particularly when the matrix is strictly triangular. We provide a conjecture for this case that extends to n×n matrices for n ≥ 3 and also provide sample code for generating the numerical range.

Comparing the operator norms of symmetric matrices sharing the same numerical range

Numerical and spectral radius of weakly⁎ measurable families of Hilbert space operators

On the ellipticity of the higher rank numerical range

Matrices with all diagonal entries lying on the boundary of the numerical range