Compact composition operators with symbol a universal covering map onto a multiply connected domain

Composition Operators with Multivalent Symbol∗

If φ is an analytic map of the unit diskD into itself, the composition operator Cφ on the Hardy space H (D) is defined by Cφ(f) = f ◦ φ. For a certain class of composition operators with multivalent symbol φ, we identify a subspace of H(D) on which C∗ φ behaves like a weighted shift. We reproduce the description of the spectrum found in [5] and show for this class of composition operators that ...

Adjoints of composition operators with rational symbol

Building on techniques developed by Cowen and Gallardo-Gutiérrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H2. We consider some specific examples, comparing our formula with several results that were previously known. 1. Preliminaries Let D denote the open unit disk in the complex plane. The Hardy space H is the Hilbert ...

Toeplitz Operators in Multiply Connected Regions

Shortest path in a multiply-connected domain having curved boundaries

Computing shortest path, overcoming obstacles in the plane, is a well-known geometric problem. However, widely assumed obstacles are polygonal in nature. Very few papers have focused on the curved obstacles, and in particular, for curved multiplyconnected domains (domains having holes). Given a set of parametric curves forming a multiply-connected domain (MCD), with one closed curve acting as a...

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...