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 R.
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.