Data: sexta-feira, 16 de dezembro de 2022, às 9h30.
Palestrante: Adi Tcaciuc (MacEwan University)
Título: Rank-one perturbations of quasinilpotent operators
Resumo: The Invariant Subspace Problem (ISP) is one of the most famous problems in Operator Theory, and is concerned with the search of non-trivial, closed, invariant subspaces for bounded operators acting on a separable Banach space. Considerable success has been achieved over the years both for the existence of such subspaces for many classes of operators, as well as for non-existence of invariant subspaces for particular examples of operators. Quasinilpotent operators are the ones for which zero is the only value in the spectrum. While there are counterexamples to ISP for quasinilpotent operators on non-reflexive Banach spaces, the ISP for quasinilpotent operators is still open in the reflexive case. In this talk, I will present an approach to the ISP for quasinilpotent operators by examining the stability of the spectrum under rank-one perturbations.