Compact intertwining relations for composition operators on $H^\infty$ and the Bloch spaces

TL;DR

This paper investigates the compact intertwining relations between composition operators and Volterra type operators on the spaces of bounded analytic functions and the Bloch space, providing new insights into their structural interactions.

Contribution

It introduces new compact intertwining relations involving collections of composition and Volterra operators on $H^$ and Bloch spaces, expanding understanding of their operator interactions.

Findings

Characterization of compact intertwining relations for composition and Volterra operators.

Identification of conditions under which these operators intertwine compactly.

Extension of known results to broader classes of operators and spaces.

Abstract

On the space of bounded analytic functions and the Bloch space on the unit disk, we study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators. Further, we consider the compact intertwining relations, which are between the whole collection of composition operators and some Volterra operator, and the whole collection of bounded Volterra operators and some composition operator.