Abstract
If G is any region in the complex plane and HP (G), 1≦p≦∞, denotes the Hardy space of analytic functions on G, then the principal aim of this paper is to present the spectral properties of the multiplication operators Mϕ defined on HP(G) by Mϕf=ϕf, where ϕ is any bounded analytic function on G. In order to do this, the speccial case in which G is bounded and ϕ(z)=z is studied in detail. In addition an operator called the truncation operator that is not a multilication operator and acts on the Hardy spaces of regions of the form ℂ/K for a compact set K is studied.
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