ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIV, 2 (2005)
p. 259 - 272

Some Properties of Composition Operators on the Dirichlet Space
G. A. Chacon and G. R. Chacon

Abstract. In this paper we investigate composition operators induced on the Dirichlet space by linear fractional maps. We characterize the essential normality in this setting, obtain conditions for the linear fractional symbols j and y of the unit disc for which Cj Cy * or Cy *Cj   is compact, and investigate the shape of the numerical range for linear fractional composition operators induced on the Dirichlet space.

Keywords:   Composition operators, compact composition operators, Dirichlet space, essentially normal operators, numerical range.

AMS Subject classification:  Primary: 47B33; Secondary: 30H05.


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