Non-compact composition operators

Compact composition operators on certain analytic Lipschitz spaces

We investigate compact composition operators on ceratin Lipschitzspaces of analytic functions on the closed unit disc of the plane.Our approach also leads to some results about compositionoperators on Zygmund type spaces.

Compact composition operators on BMOA(Bn)

Dedicated to Professor T.-D. Zhong on the occasion of his 80th birthday Abstract: The paper gives some characterization theorems for the compact composition operator on some function spaces. In particular, it gives a characterization for compact composition operators on BMOA(Bn) with Bn being the unit ball in C , which generalizes a result proved by Bourdon, Cima and Matheson for the case n = 1...

Representing non–weakly compact operators

For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E/E) is defined by R(S)(x + E) = Sx + E (x ∈ E). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W (E) (here W (E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non–zero compact...

Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

Strongly compact algebras associated with composition operators

An algebra of bounded linear operators on a Hilbert space is called strongly compact whenever each of its bounded subsets is relatively compact in the strong operator topology. The concept is most commonly studied for two algebras associated with a single operator T : the algebra alg(T ) generated by the operator, and the operator’s commutant com(T ). This paper focuses on the strong compactnes...