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Abstract. Various operator theoretic properties of composition operators with linear fractional symbol acting on the Dirichlet space of the unit ball are discussed. Furthermore, we use Calderón's complex interpolation to investigate the spectrum of composition operators with automorphic symbol acting on the analytic Besov spaces of the ball and on the weighted Dirichlet spaces of the ball, which include the Dirichlet, Arveson, Hardy and Bergman spaces.
AMS Subject Classification
(1991): 47B33, 46B70
Keyword(s):
composition operator,
Dirichlet space,
Besov space,
spectrum,
complex interpolation
Received December 1, 2009. (Registered under 6408/2009.)
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