González-Mercado, Elikin Y.

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Subespacios invariantes de funciones analíticas
(2005) González-Mercado, Elikin Y.; Salas-Olaguer, Héctor N.; College of Arts and Sciences - Sciences; Rózga, Krzysztof; Barety, Julio; Department of Mathematics; Walker-Ramos, Uroyoán
The present work is concerned with several results obtained by Arne Beurling for invariant subspaces of the operator “multiplication by z”, that is, the operator Mz(f (z))= zf (z), where f (z)∈H2(D), H2 (D) is the space of Hardy, z∈D, z and D is the unit circle z <1.There are two problems relating to the operators T and T* , defined on a Hilbert space H which are the starting point for studying the invariant subspaces of Mz . These are called the closure and extinction problems, T* and T , respectively. The solution to the closure problem is that the invariant subspaces of Mz in Hardy space are the subspaces φH2 (D), where φ is an inner function on H2 (D). The extinction problem is related to the invariant subspaces of the operator M*z . Finally, z we analyzed Sarason’s approach to the characterization of invariant subspaces of Volterra operator.