Linear fractional composition operators on the Dirichlet space in the unit ball

We investigate the adjoints of linear fractional composition operators Cϕ acting on classical Dirichlet space D(BN) in the unit ball BN of ℂN, and characterize the normality and essential normality of Cϕ on D(BN) and the Dirichlet space modulo constant function D0(BN), where ϕ is a linear fractional map ϕ of BN. In addition, we also show that for any non-elliptic linear fractional map ϕ of BN, the composition maps σ o ϕ and ϕ o σ are elliptic or parabolic linear fractional maps of BN.