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Sarita Ojha

Publications and source records attributed to Sarita Ojha.

11 recordsLinked to original sources
arXiv2026

On the shape of the numerical range of some tridiagonal matrices

In this paper, we study the elliptical shape of the numerical range of tridiagonal matrices of orders $3,4$ and $5$ with zero entries on the main diagonal, a positive constant value $a$ along the super-diagonal, and sub-diagonal entries are \begin{align*} \begin{cases} r, sr^2, r^3, sr^4,\ldots, r^{n-1} & \mbox{ if $n$ is even, and } r, sr^2, r^3, sr^4,\ldots, sr^{n-1} & \mbox{ if $n$ is odd}, \end{cases} \end{align*} where $n$ denotes the order of the matrix, $s>0$ and $r$ is a real number. We further investigate the flat portions on the boundary of the numerical range of these $n\times n$ matrices in the special case $r=-1$. Some results given in \cite{chien2011numerical} are obtained as a particular case of our results.

math.FA↗
arXiv2026

Numerical range and invariant subspaces of weighted composition operators on the Hardy space of Dirichlet series

In this paper, we study various results on numerical range of weighted composition operators on Hardy space of Dirichlet series. Certain conditions are provided under which the numerical range contains zero and some circular or elliptic disks. With the help of invariant subspaces of the operator, we also determine the numerical range of reductive weighted composition operators on this space. Additionally, we discuss some results on the Davis-Wielandt shell of composition operators with some natural questions that arise from our findings.

math.FA↗
arXiv2026

On the numerical radius of a class of weighted shift operators

In this paper, we derive some bounds on numerical radius of the weighted shift operator $T$ with weights $(1,sq,q^2,tq^3,q^4,sq^5,q^6,tq^7,\ldots)$ where $s,t >0$ and $0<q<1$. Furthermore, we provide an entire function $F_T(z)$. The reciprocal of the minimal positive root of $F_T(z)=0$ gives the numerical radius of $T$. These results generalize several previously known results on the numerical radius of weighted shift operators discussed in \cite{chakraborty2025numerical}.

math.FA↗
arXiv2026

Improved upper bounds for the Berezin numbers of operators on reproducing kernel Hilbert spaces

In this article, several upper bounds for the Berezin numbers of bounded linear operators on reproducing kernel Hilbert spaces are obtained through the use of interpolation paths of symmetric means and Orlicz functions. With suitable selections of these paths and functions, we show that the results presented here refine and generalize several earlier known findings. Furthermore, we derive some Berezin number inequalities for such operators using refined Young's inequalities.

math.FA↗
arXiv2026

Estimation of $\mathrm{A}$-Berezin number and $\mathrm{A}$-Berezin norm inequalities via Moore-Penrose inverse

In this article, we establish the $A$-Berezin number and $A$-Berezin norm inequalities for bounded linear operators on a reproducing kernel Hilbert space using the Moore-Penrose inverse. We further extend these inequalities to the case of the sum of two bounded linear operators. As an application, upper bounds of the Berezin number and Berezin norm of block matrices have been discussed via the Moore-Penrose inverse. The inequalities established here offer both refinements and generalizations of previous results.

math.FA↗
arXiv2026

On posinormality of weighted composition-differentiation operators on $H^2(\mathbb{D})$

In this article, the posinormality and coposinormality of weighted composition-differentiation operators on Hardy space $H^2(\mathbb{D})$ are investigated. It is observed that while a composition-differentiation operator $D_{ϕ,n}$ fails to be posinormal, the weighted composition-differentiation operator $D_{ψ,ϕ,n}$ can be posinormal for specific choices of $ψ, ϕ$. Some necessary conditions are obtained for posinormality and coposinormality of the operator $D_{ψ,ϕ,n}$. Furthermore, the adjoint formula for this operator is derived which also helped us to examine some results regarding posinormality of this operator.

math.FA↗
arXiv2026

Iterated Aluthge transforms of some composition operators on weighted Bergman spaces

In this paper, we compute the iterated Aluthge transforms $\widetilde{C_ϕ}^{(n)}$ of the composition operator $C_ϕ$ on the weighted Bergman spaces $\mathcal{A}_α^2(\mathbb{D})$, where $ϕ(z)=az+(1-a)$ for $0<a<1$. Also, we obtain the norm and numerical radius of $\widetilde{C_ϕ}^{(n)}$ on $\mathcal{A}_α^2(\mathbb{D})$. We establish that $\widetilde{C_ϕ}^{(n)}$ converges in the strong operator topology on $\mathcal{A}_α^2(\mathbb{D})$. The purpose of this paper is to examine the results of \cite{jung2015iterated} for the weighted Bergman spaces $\mathcal{A}_α^2(\mathbb{D})$. Additionally, by using the iterated Aluthge transforms of $C_ϕ^*$ on $\mathcal{A}_α^2(\mathbb{D})$, we derive the iterated Aluthge transforms of $C_σ$, where $\displaystyleσ(z)=\frac{az}{-(1-a)z+1}$ for $0<a<1$, on some weighted Hardy space $H^2(β_α)$ and study its convergence. Finally, we raise some questions that emerge from these findings.

math.FA↗
arXiv2016

Weighted $βγ$-summability of fuzzy functions of order $θ$

The concept of weighted $βγ$ - summability of order $θ$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found some suitable conditions to get its relation with the generalized statistical convergence. Finally we have proved a generalized version of Tauberian theorem.

math.GM↗
arXiv2015

Certain properties of bounded variation of sequences of fuzzy numbers by using generalized weighted mean

The class of bounded variation $bv^F(u,v)$ of fuzzy numbers introduced by [8] has been investigated further with the help of the generalized weighted mean matrix $G(u,v)$. Imposing some restrictions on the matrix $G(u,v)$, we have established it's relation with different class of sequences such as our known classical sets, set of all statistically null difference sequences, Cesaro sequences etc. Also we have examined the concepts like equivalent fuzzy number, symmetric fuzzy number on this quasilinear space.

math.GM↗
arXiv2015

Some characterizations on weighted $αβ$-statistical convergence of fuzzy functions of order $θ$

Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $αβ$ - statistical convergence of order $θ$ in case of fuzzy functions and classified it into pointwise, uniform and equi-statistical convergence. We have checked some basic properties and then the convergence are investigated in terms of their $α$-cuts. The interrelation among them are also established. We have also proved that continuity, boundedness etc are preserved in the equi-statistical sense under some suitable conditions, but not in pointwise sense.

math.GM↗