Compositional number concepts in children: The role of base-5 numeral structures in Sign language.

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

This paper introduces a novel and versatile framework for numerical radius inequalities within complex Hilbert spaces, building upon the generalized real and imaginary parts of an operator defined by Kittaneh and Stojiljković [Kittaneh F, Stojiljković V. New generalized numerical radius inequalities for Hilbert space operators. J Inequal Appl. 2026: 25. doi:10.1186/s13660-026-03438-3]. We define a new generalized numerical radius, w h , g Re ( A ) , and show its properties as a norm on the C ∗ -algebra of bounded linear operators, B ( H ) , under specified conditions. The proposed framework encompasses existing definitions and generalizations, yielding new identities and refined bounds for w h , g Re ( A ) . The adaptability of w h , g Re ( A ) through the functions h and g allows it to reduce to well-known inequalities already established in the literature, including those by Sheikhhosseini et al. [Sheikhhosseini A, Khosravi M, Sababheh M. The weighted numerical radius. Ann Funct Anal. 2022;13:3. doi:10.1007/s43034-021-00148-3] and Kittaneh [Kittaneh F. Numerical radius inequalities for Hilbert space operators. Studia Math. 2005;168:73–80. doi: 10.4064/sm168-1-5]. The work further explores various inequalities, including those involving powers of operators and operator matrices, providing extensions and refinements to previous results in the field.

In this paper, we study $(\alpha ,\beta )$-A-normal tuples of operators acting on semi-Hilbertian spaces, that is, Hilbert-like spaces endowed with a positive bounded operator A inducing a semi-inner product. By exploiting the geometric structure associated with A, we establish several operator inequalities and norm estimates that characterize this class of operator tuples. An A-characterization of $(\alpha ,\beta )$-A-normal tuples is obtained, and their stability properties are investigated. In particular, we show that this class is stable under the A-adjoint, invariant under similarity transformations induced by A-unitary operators, and stable under sums and products under suitable conditions. These results extend a number of classical inequalities from the Hilbert space setting to the semi-Hilbertian framework and contribute to the development of multivariable operator inequalities, with potential applications to joint spectral theory and numerical radius estimates.

In anti-slide structures with continuous ladders (hereinafter referred to as ASCLs), horizontal and vertical reinforced concrete anti-slide members are connected head-to-tail in a ladder-like configuration, positioned along the sliding surfaces of slopes. The anti-slide members are interconnected and anchored from the sliding mass through the sliding zone into the underlying intact bedrock, so as to resist the landslide thrust and replace the weak materials within the sliding zone. By improving the load arrangement, the structural stress of the horizontal anti-slide members, and landslide thrust calculation of ASCLs, numerical extreme values of the axial force, shear force and bending moment were verified in a reasonable numerical range via the extreme values of the analytical and modified analytical results. The extreme value of the axial force of the modified analytical calculation result was between the analytical and numerical results. The maximum modified analytical calculation result of the shear force was between the analytical and numerical results, and the minimum modified analytical calculation result of the shear force was relatively close to the analytical and numerical results. The extreme modified analytical calculation result of the bending moment of the ASCLs was between the analytical and numerical results. The correctness of the numerical calculation results was well verified via the analytical and modified analytical results.