Operators on spaces of analytic functions
Tom 108 / 1994
Studia Mathematica 108 (1994), 49-54
DOI: 10.4064/sm-108-1-49-54
Streszczenie
Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.
