A note on fractional difference operators

A Note on Weighted Composition Operators on L^p-Spaces

A monotonicity result for discrete fractional difference operators

In this note we demonstrate that if y(t) ≥ 0, for each t in the domain of t → y(t), and if, in addition, Δ0y(t) ≥ 0, for each t in the domain of t → Δ0y(t), with 1 < ν < 2, then it holds that y is an increasing function of t. This demonstrates that, in some sense, the positivity of the νth order fractional difference has a strong connection to the monotonicity of y. Furthermore, we provide a du...

On Some Fractional Systems of Difference Equations

This paper deal with the solutions of the systems of difference equations $$x_{n+1}=frac{y_{n-3}y_nx_{n-2}}{y_{n-3}x_{n-2}pm y_{n-3}y_n pm y_nx_{n-2}}, ,y_{n+1}=frac{y_{n-2}x_{n-1}}{ 2y_{n-2}pm x_{n-1}},,nin mathbb{N}_{0},$$ where $mathbb{N}_{0}=mathbb{N}cup left{0right}$, and initial values $x_{-2},, x_{-1},,x_{0},,y_{-3},,y_{-2},,y_{-1},,y_{0}$ are non-zero real numbers.

A note on $lambda$-Aluthge transforms of operators

Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...