The Spectra And Normality Of (Weighted) Composition Operators On Some Analytic Function Spaces

LetΩbe a bounded domain in a complex space or a Banach space.φis an analytic selfmap ofΩ. u is an analytic function onΩ. For f is an element in an analytic function space, the composition operator induced byφis defined as Cφ(f)= f(?)φ. The weighted composition operator uCφis defined as uCφ(f)= u·f(?)φ.In this thesis, we considerΩas the unit disk of the complex plane, or the unit ball of the complex space, or the unit ball of a Banach space. On the analytic function space ofΩ, we investigate the spectra and normality of composition operators and weighted composition operators. We give the spectra of weighted composition operators. We also characterize the conditions of normality and essential normality of linear fractional composition operators in elliptic, parabolic and hyperbolic types.To get the normality conditions, the linear fractional maps are analyzed. Some results about linear fractional maps are obtained. We show that the non-elliptic linear fractional maps compose with the adjoint maps are elliptic or parabolic linear fractional maps.