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View article: A Function-Sharing Criterion for Normal Functions
A Function-Sharing Criterion for Normal Functions Open
In this paper, we present a function-sharing criterion for the normality of meromorphic functions. Let $f$ be a meromorphic function in the unit disc $\mathbb{D}\subset \mathbb{C}$, $ψ_1$, $ψ_2$, and $ψ_3$ be three meromorphic functions in…
View article: Ascent and Descent of Weighted Composition Operators on Lorentz spaces
Ascent and Descent of Weighted Composition Operators on Lorentz spaces Open
The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation $T$ and the complex-valued measurable function $u$ defined on m…
View article: On Compression of Generalized Slant Toeplitz Operators to H2(𝕋n)
On Compression of Generalized Slant Toeplitz Operators to H2(𝕋n) Open
In the paper, we introduce the notion of compression of generalized slant Toeplitz operators to the Hardy space of n-dimensional torus T n .It deals with characterizations of introduced operator with specific as well as general symbols.Cer…
View article: Multivariate analogue of slant Toeplitz operators
Multivariate analogue of slant Toeplitz operators Open
This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on the Lebesgue space of the $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ and $n\geq 1$. We obtain certain equivalent co…
View article: On weighted generalized composition operators on weighted hardy spaces
On weighted generalized composition operators on weighted hardy spaces Open
The present paper introduces the class of weighted generalized composition operators of higher order defined on the weighted Hardy spaces. The study of bounded operators belonging to this class is undertaken and an attempt is made to descr…
View article: Slant Toeplitz Operators on the Lebesgue Space of the Torus
Slant Toeplitz Operators on the Lebesgue Space of the Torus Open
This paper introduces the class of slant Toeplitz operators on the Lebesgue space of the torus. A characterization of these operators as the solutions of an operator equation is obtained. The paper describes various algebraic properties of…
View article: Essentially generalized lambda-slant Hankel operators
Essentially generalized lambda-slant Hankel operators Open
The notion of an essentially generalized λ-slant Hankel operator of kth-order on the space L2 is introduced and its algebraic properties are discussed. The study is further carried to compression and essentially compression of generalized …
View article: Essentially generalized $λ$-slant Toeplitz operators
Essentially generalized $λ$-slant Toeplitz operators Open
We introduce the notion of an essentially generalized $λ$-slant Toeplitz operator on the Hilbert space $L^2$ for a general complex number $λ$, via the operator equation $λM_{z}X - XM_{z^{k}} = K$, $K$ being a compact operator on $L^2$ and …
View article: Toeplitz and weighted Toeplitz operators on weighted sequence spaces
Toeplitz and weighted Toeplitz operators on weighted sequence spaces Open
Weighted Toeplitz operator Tφβ on H2(β) with φ ∈ L∞(β) is defined as Tφβ = Pβ Mφβ, where Pβ is the orthogonal projection of L2(β) onto H2(β). The paper describes some properties of weighted Toeplitz operators induced by some specific symbo…
View article: A generalization of $\lambda-$slant Toeplitz operators
A generalization of $\lambda-$slant Toeplitz operators Open
We compute and study the behavior of the solutions of the equation $\\lambda M_{z} X = X M_{{z}^k}$, which are referred as generalized $\\lambda -$slant Toeplitz operators, for general complex number $\\lambda$ and $k \\geq 2$.
View article: Operator equations and Spectral Problems
Operator equations and Spectral Problems Open
The multiplication operators are the linear operators induced by multiplication by some fixed function. One of the important fact which motivates the study of multiplication operators is that every normal operator is similar to a multiplic…