Mathematische Annalen

, Volume 327, Issue 1, pp 117–134

Adjoints of linear fractional composition operators on the Dirichlet space

  • Eva A. Gallardo-Gutiérrez
  • Alfonso Montes-Rodríguez
Article

DOI: 10.1007/s00208-003-0442-9

Cite this article as:
Gallardo-Gutiérrez, E. & Montes-Rodríguez, A. Math. Ann. (2003) 327: 117. doi:10.1007/s00208-003-0442-9

Abstract.

The adjoint of a linear fractional composition operator acting on the classical Dirichlet space is expressed as another linear fractional composition operator plus a two rank operator. The key point is that, in the Dirichlet space modulo constant functions, many linear fractional composition operators are similar to multiplication operators and, thus, normal. As a particular application, we can easily deduce the spectrum of each linear fractional composition operator acting on such spaces. Even the norm of each linear fractional composition operator is computed on the Dirichlet space modulo constant functions. It is also shown that all this work can be carried out in the Hardy space of the upper half plane.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Eva A. Gallardo-Gutiérrez
    • 1
  • Alfonso Montes-Rodríguez
    • 2
  1. 1.Departamento de MatemáticasUniversidad de CádizPuerto Real (Cádiz)SPAIN
  2. 2.Departamento de Análisis MatemáticoUniversidad de SevillaSPAIN