Geodesic
Operators on spaces of analytic functions
Studia Mathematica, Tome 108 (1994) no. 1, pp. 49-54

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-108-1-49-54
Keywords: spaces of analytic functions, polynomially bounded, multipliers, spectral properties, cyclic subspace

K. Seddighi 1

1 
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K. Seddighi. Operators on spaces of analytic functions. Studia Mathematica, Tome 108 (1994) no. 1, pp. 49-54. doi: 10.4064/sm-108-1-49-54

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