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Alemeh Sheikhhosseini

Publications and source records attributed to Alemeh Sheikhhosseini.

5 recordsLinked to original sources
arXiv2026

A Comparison of some Weighted Numerical Radii of Hilbert Space Operators

In recent years, several generalizations of the numerical radius for bounded linear operators on Hilbert spaces have been introduced and extensively studied. These generalizations provide refined tools for investigating operator inequalities and spectral properties. In this paper, we investigate several generalized numerical radii and establish relationships among them. We also establish several relationships among these generalized numerical radii and show that the $(s,t)$-weighted numerical radius can be represented as a rescaled form of the $t$-weighted numerical radius.

math.FA↗
arXiv2026

Weighted numerical radii of accretive matrices

In this paper, we consider the notion of the weighted numerical radius, denoted by $ ω_ν(A)$, for the class of accretive matrices, where \\ $ ν\in [0, 1].$ This notion generalizes both the classical numerical radius and the operator norm. All of the obtained inequalities reduce to the corresponding classical inequalities when $ ν=1/2 $ or when the matrix is positive definite.

math.FA↗
arXiv2025

The Resolvent Mean and The Parametrized $\mathcal{A} \sharp \mathcal{B}$

Resolvent average and weighted \(\mathcal{A}\sharp \mathcal{H}\)-mean have been defined recently for positive definite matrices. Since the class of accretive matrices provides a general framework for addressing certain known results on positive matrices, this paper extends the notions of resolvent average and the weighted \(\mathcal{A}\sharp \mathcal{H}\)-mean to accretive matrices and discusses some of their properties.\\ The obtained results happen to be legitimate generalizations of those known results on positive definite matrices.\\ Among many results, we show that if $A,B$ are positive definite matrices, and $0\leqλ\leq 1, μ>0$, then \[\mathcal{R}_μ(A,B,1-λ,λ)+μI \geq C \Big(A \sharp_{\bmλ} B +μI\Big),\] where $\mathcal{R}_λ$ is the resolvent average, $\sharp_{\bmλ}$ is the weighted geometric mean and $I$ is the identity matrix, for some positive constant $C$; as a new relation between the resolvent average and the geometric mean.

math.FA↗