Composition operator
From Wikipedia, the free encyclopedia
- For information about the operator "o" of composition, see function composition or composition of relations.
In mathematics, the composition operator Cφ with symbol φ is defined by the rule
where 
denotes function composition. The domain of a composition operator is usually taken to be some Banach space, often consisting of holomorphic functions: for example, some Lp space, Hardy space or Bergman space. Interesting questions posed in the study of composition operators often relate to how the spectral properties of the operator depend on the function space. Other questions include whether Cφ is compact or trace-class; answers typically depend on how the function φ behaves on the boundary of some domain.
The study of composition operators is covered by AMS category 47B33.
[edit] References
- J. Shapiro, Compact composition operators on spaces of boundary-regular holomorphic functions. (1987) Proc. AMS, 100, 49-57.
