Operators on spaces of analytic functions

K. Seddighi

ArticleOriginal scientific text

Title

Operators on spaces of analytic functions

Authors ¹

Affiliations

Department of Mathematics & Statistics, College of Sciences, Shiraz University, Shiraz 71454, Islamic Republic of Iran

Abstract

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} ∥ \leq 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.

Keywords

ENG

spaces of analytic functions, polynomially bounded, multipliers, spectral properties, cyclic subspace

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Title

Operators on spaces of analytic functions

Affiliations

Abstract

Keywords

Bibliography