Adi Tcaciuc: The Invariant Subspace Problem for rank-one perturbations.

Data: segunda-feira, 22 de abril de 2019, às 10h00.

Sala: A249

Adi Tcaciuc (MacEwan University)

Título: The Invariant Subspace Problem for rank-one perturbations.

Resumo:  The Invariant Subspace Problem is one of the most famous   problem 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. However, for the most  important case of a separable Hilbert space, the problem is still open.
A natural, related  question deals with the existence of invariant   subspaces for perturbations of bounded operators. These type of  problems have been studied for a long time, mostly in the Hilbert  space setting. In this talk I will present a new approach to these  “perturbation” questions,  in the more general setting of a separable  
Banach space.  I will focus on the  recent history, presenting several  new results that were obtained  along the way with this new approach,  and examining their connection and relevance to the Invariant Subspace  Problem.