New York Journal of Mathematics
Volume 17a (2011) 193-212


M. Carlsson

On the Beurling-Lax theorem for domains with one hole

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Published: January 30, 2011
Keywords: Subnormal operators, index, bundle shifts, Beurling Lax theorem.
Subject: Primary 47B20, Secondary 46E40

We consider pure subnormal operators T of the type studied in Carlsson, 2011, with the additional requirement that σ(T) has one hole. If ind(T-λ0)=-n for some λ0 and n∈N, we show that the operator can be decomposed as T=⊕k=1n Tk, where each Tk satisfies ind(T-λ0)=-1, thus extending the classical Beurling-Lax theorem (in which σ(T) is the unit disc). We also provide a set of unitary invariants that completely characterize T and study the model spaces for the simpler operators Tk.


This research was supported by the Swedish research council (2008-23883-61232-34) and the Swedish Foundation for International Cooperation in Research and Higher Education (YR2010-7033).

Author information

Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307, Correo-2, Santiago, Chile