A Note on Equicontiuity of Families of Operators and Automorphisms

A Note on Equicontinuity 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 a one parameter group of automorphisms 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.

A Note on Absolute Central Automorphisms of Finite $p$-Groups

Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study  some properties of absolute central automorphisms of a given finite $p$-group.

On C0-Group of Linear Operators

In this paper we consider C0-group of unitary operators on a Hilbert C*-module E. In particular we show that if A?L(E) be a C*-algebra including K(E) and ?t a C0-group of *-automorphisms on A, such that there is x?E with =1 and ?t (?x,x) = ?x,x t?R, then there is a C0-group ut of unitaries in L(E) such that ?t(a) = ut a ut*.

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 Weighted Composition Operators on L^p-Spaces