Abstract
This chapter describes some factorization properties of composition operators. The central topic in the study of composition operators on Hardy spaces (as well as on various other function spaces) is the investigation of the interplay between properties of the generating function φ and properties of the operator C φ on the spaces under consideration. β-order bounded composition operators can be characterized by means of a factorization scheme in which one of the factors is a Hilbert–Schmidt operator.
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