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Operadores esencialmente normales y existencia de subespacios invariantes
(2021-06-28)
A main problem of Operator Theory consists of studying which operators have an invariant subspace, or what properties they must have to possess it. In this project we will work on separable complex Hilbert spaces and we ...
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Operadores universales y subespacios invariantes
(2019)
The Invariant Subspace Problem is one of the most studied problems on Operator Theory in the last decades. In fact, it is still open in the Hilbert space setting. The purpose of this work is to present the most classic ...
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La desigualdad de Von Neumann y la teoría de dilatación
(2018-09)
A famous inequality by von Neumann states that if T is a contraction on a Hilbert space and p is a polynomial, then kp(T)k ≤ sup{|p(z)| : z ∈ C, |z| ≤ 1}. As time went on, this inequality has given rise to a large variety ...