Spectra of composition operators on Fock-type spaces

Abstract

This work is a continuation of our recent investigation in [15] where we characterized various topological and dynamical properties of the composition operator C acting between Fock-type spaces F^pφ and F^qφ when both exponents p and q are nite. Now we investigate the structures when at least one of the spaces is growth type and determine the spectrum of the operator C on all the Banach spaces F^pφ . The results about boundenness of C offer an interesting trichotomized insight into structures of the symbol . Some of the resuts obtained are also new on the corresponding classical Fock spaces.

Key words: Generalized Fock spaces, bounded, compact, composition, spectrum, connected, isolated, essential norm, extremal, supercyclic, hypercyclic.