Topological Structure of the Space of Composition Operators Between Different Fock Spaces

Abstract

In this paper the topological structure problem for the space of composition operators acting from a Fock space F p (C n ) to another one F q (C n ) with 0 < p, q ≤ ∞ is completely solved. Explicit descriptions of all (path) components and isolated points in this space are obtained.

Topological structure of the space of composition operators on $L^\infty$ of an unbounded, locally finite metric space

“…While the solutions to these problems still elude mathematicians in the H 2 (D) setting, much work has been done to solve the problems for other spaces X of analytic functions on D. Manhas provides a survey in [18] of the work on topological structures of composition operators and weighted composition operators on various spaces including the Bergman space, Dirichlet space, Bloch space and weighted Banach space of analytic functions. The topological structure of (weighted) composition operators between different spaces has also been studied (see [10,13,15]). This work has migrated to Banach spaces of holomorphic functions in several complex variables as well; see [23,11] for examples of such.…”