Álvarez-Pardo, Edgardo

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Subespacios invariantes de algunos operadores
(2004) Álvarez-Pardo, Edgardo; Salas-Olaguer, Héctor N.; College of Arts and Sciences - Sciences; Rózga, Krzysztof; Barety, Julio; Department of Mathematics; Seguel, Jaime
In the following dissertation a number of results are received and presented. First the results obtained by Aronszajn-Smith and J Wermer concerning invariant subspaces of compact operators are received. Other bounded operators with special characteristic are also presented. Metric projections on Banach spaces are defined. Then lower limit of a sequence of closed subspaces of infinite dimensional Banach space and the relation between this and invariant subspaces are defined as well lomonosov’s method to obtained proper invariant subspaces common to a family of operators that commute with respect to a compact operator is presented. Finally, it is shown that if T is a invertible bounded operator on Banach space such that Tn ,n∈Z, does not grow too rapidly and whose spectrum contains more than one point, then T has a nontrivial invariant subspace.