A Note on Uniform Operators

Uniform Boundedness Principle for operators on hypervector spaces

The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.

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

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...  

A Note on Strong Dinaturality, Initial Algebras and Uniform Parameterized Fixpoint Operators

I show a basic Yoneda-like lemma relating strongly dinatural transformations and initial algebras. Further, I apply it to reprove known results about unique existence of uniform parameterized fixpoint operators.

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 Equicontiuity of Families of Operators and Automorphisms

This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H , and of families of maps on B(H). It is shown that the a one parameter group is uniformly equicontinuous if and only if the group of unitaries which implements it is so. A “geometrical” necessary and sufficient condition is given for a family of operators to be uniformly equicontinuous.