arXiv subjects

A. Zamani

Publications and source records attributed to A. Zamani.

9 recordsLinked to original sources

arXiv2022

An extension of Birkhoff--James orthogonality relations in semi-Hilbertian space operators

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given a positive operator $A\in\B(\h)$, and a number $λ\in [0,1]$, a seminorm ${\|\cdot\|}_{(A,λ)}$ is defined on the set $\B_{A^{1/2}}(\h)$ of all operators in $\B(\h)$ having an $A^{1/2}$-adjoint. The seminorm ${\|\cdot\|}_{(A,λ)}$ is a combination of the sesquilinear form ${\langle \cdot, \cdot\rangle}_A$ and its induced seminorm ${\|\cdot\|}_A$. A characterization of Birkhoff--James orthogonality for operators with respect to the discussed seminorm is given. Moving $λ$ along the interval $[0,1]$, a wide spectrum of seminorms are obtained, having the $A$-numerical radius $w_A(\cdot)$ at the beginning (associated with $λ=0$) and the $A$-operator seminorm ${\|\cdot\|}_A$ at the end (associated with $λ=1$). Moreover, if $A=I$ the identity operator, the classical operator norm and numerical radius are obtained. Therefore, the results in this paper are significant extensions and generalizations of known results in this area.

math.FA↗

arXiv2022

An orthogonality relation in complex normed spaces based on norm derivatives

Let $X$ be a complex normed space. Based on the right norm derivative $ρ_{_{+}}$, we define a mapping $ρ_{_{\infty}}$ by \begin{equation*} ρ_{_{\infty}}(x,y) = \frac1π\int_0^{2π}e^{iθ}ρ_{_{+}}(x,e^{iθ}y)dθ\quad(x,y\in X). \end{equation*} The mapping $ρ_{_{\infty}}$ has a good response to some geometrical properties of $X$. For instance, we prove that $ρ_{_{\infty}}(x,y)=ρ_{_{\infty}}(y,x)$ for all $x, y \in X$ if and only if $X$ is an inner product space. In addition, we define a $ρ_{_{\infty}}$-orthogonality in $X$ and show that a linear mapping preserving $ρ_{_{\infty}}$-orthogonality has to be a scalar multiple of an isometry. A number of challenging problems in the geometry of complex normed spaces are also discussed.

math.FA↗

arXiv2021

Operational Learning-based Boundary Estimation in Electromagnetic Medical Imaging

Incorporating boundaries of the imaging object as a priori information to imaging algorithms can significantly improve the performance of electromagnetic medical imaging systems. To avoid overly complicating the system by using different sensors and the adverse effect of the subject's movement, a learning-based method is proposed to estimate the boundary (external contour) of the imaged object using the same electromagnetic imaging data. While imaging techniques may discard the reflection coefficients for being dominant and uninformative for imaging, these parameters are made use of for boundary detection. The learned model is verified through independent clinical human trials by using a head imaging system with a 16-element antenna array that works across the band 0.7-1.6 GHz. The evaluation demonstrated that the model achieves average dissimilarity of 0.012 in Hu-moment while detecting head boundary. The model enables fast scan and image creation while eliminating the need for additional devices for accurate boundary estimation.

cs.CV↗

arXiv2019

Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces

Let $A$ be a positive bounded operator on a Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$. The semi-inner product ${\langle x, y\rangle}_A := \langle Ax, y\rangle$, $x, y\in\mathcal{H},$ induces a seminorm ${\|\cdot\|}_A$ on $\mathcal{H}$. Let ${\|T\|}_A,\ w_A(T),$ and $c_A(T)$ denote the $A$-operator seminorm, the $A$-numerical radius, and the $A$-Crawford number of an operator $T$ in the semi-Hilbertian space $\big(\mathcal{H}, {\|\cdot\|}_A\big)$, respectively. In this paper, we present some seminorm inequalities and equalities for semi-Hilbertian space operators. More precisely, we give some necessary and sufficient conditions for two orthogonal semi-Hilbertian operators satisfy Pythagoras' equality. In addition, we derive new upper and lower bounds for the numerical radius of operators in semi-Hilbertian spaces. In particular, we show that \begin{align*} \frac{1}{16} {\|TT^{\sharp_{A}} + T^{\sharp_{A}}T\|}^{2}_{A} + \frac{1}{16}c_{A}\Big(\big(T^2 + (T^{\sharp_{A}})^2\big)^2\Big) \leq w^4_{A}(T) \leq \frac{1}{8} {\|TT^{\sharp_{A}} + T^{\sharp_{A}}T\|}^{2}_{A} + \frac{1}{2}w^2_{A}(T^2), \end{align*} where $T^{\sharp_A}$ is a distinguished $A$-adjoint operator of $T$. Some applications of our inequalities are also provided.

math.FA↗

arXiv2019

Numerical radius inequalities concerning with algebraic norms

We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities involving the product of two operators. Applications of our inequalities are also provided.

math.FA↗

arXiv2018

Norm-parallelism and the Davis--Wielandt radius of Hilbert space operators

We present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the Birkhoff--James orthogonality for Hilbert space operators. Moreover, we discuss the connection between norm-parallelism to the identity operator and an equality condition for the Davis--Wielandt radius. Some other related results are also discussed.

math.FA↗

arXiv2018

An extension of orthogonality relations based on norm derivatives

We introduce the relation $ρ_λ$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give a characterization of inner product spaces via the functional $ρ_λ$. Moreover, we consider a class of linear mappings preserving this new kind of orthogonality. In particular, we show that a linear mapping preserving $ρ_λ$-orthogonality has to be a similarity, that is, a scalar multiple of an isometry.

math.FA↗

arXiv2017

Orthogonality and parallelism of operators on various Banach spaces

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We consider the characterization of norm parallelism problem in p Schatten ideals and locally uniformly convex spaces. Later on, we study the case when an operator is norm parallel to the identity operator. Finally, we give some equivalence assertions about the norm parallelism of compact operators. Some applications and generalizations are discussed for certain operators.

math.FA↗

arXiv2011

Finite temperature calculations for the bulk properties of strange star using a many-body approach

We have considered a hot strange star matter, just after the collapse of a supernova, as a composition of strange, up and down quarks to calculate the bulk properties of this system at finite temperature with the density dependent bag constant. To parameterize the density dependent bag constant, we use our results for the lowest order constrained variational (LOCV) calculations of asymmetric nuclear matter. Our calculations for the structure properties of the strange star at different temperatures indicate that its maximum mass decreases by increasing the temperature. We have also compared our results with those of a fixed value of the bag constant. It can be seen that the density dependent bag constant leads to higher values of the maximum mass and radius for the strange star.

astro-ph.SR↗