On the closed range problem for composition operators on the Dirichlet space

Abstract

We characterize closed range composition operators on the Dirichlet space for a particular class of composition symbols. The characterization relies on a result about Fredholm Toeplitz operators with BMO1 symbols, and with Berezin transforms of vanishing oscillation.

Keywords

• composition operator
• dirichlet space
• toeplitz operator
• berezin transform
• closed range operator
• vanishing mean oscillation
• 47b33
• 47a53
• 30h25
• 30h35
• 30j10