Hankel Operators on Bounded Analytic Functions

James Dudziak, T. W. Gamelin, Pamela Gorkin
1999 Transactions of the American Mathematical Society  
For U a domain in the complex plane and g a bounded measurable function on U , the generalized Hankel operator Sg on H ∞ (U ) is the operator of multiplication by g followed by projection into L ∞ /H ∞ . Under certain conditions on U we show that either Sg is compact or there is an embedded ∞ on which Sg is bicontinuous. We characterize those g's for which Sg is compact in the case that U is a Behrens roadrunner domain.
doi:10.1090/s0002-9947-99-02178-9 fatcat:qra2desycrfwtgzcee3wcycyrq