A NOTE ON OPERATORS CONSISTENT IN INVERTIBILITY

Consistent in invertibility operators and SVEP

If S(X ) ⊂ B(X ), where B(X ) denotes the algebra of operators on a Banach space X , then A ∈ B(X ) is S(X ) consistent if AB ∈ S(X ) ⇐⇒ BA ∈ S(X ) for every B ∈ B(X ). SVEP is a powerful tool in determining the S(X ) consistency of operators A for various choices of the subset S(X ).

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

A Note on the Invertibility of Nonlinear ARMA models

We review the concepts of local and global invertibility for a nonlinear auto-regressive moving-average (NLARMA) model. Under very general conditions, a local invertibility analysis of a NLARMA model admits the generic dichotomy that the innovation reconstruction errors either diminish geometrically fast or grow geometrically fast. We derive a simple sufficient condition for a NLARMA model to b...

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...