Seminario di Analisi Complessa
Dipartimento di Matematica
Università di Roma Tor Vergata
Prossimi seminari:
Eva Gallardo Gutierrez, Universidad Complutense de Madrid. Compact perturbations of normal operators: invariant subspaces, spectral idempotents and decomposability
Giovedì 2 Maggio ore 16 aula Dal Passo
Abstract:
After addressing the problem regarding the existence of non-trivial closed invariant subspaces of finite-rank perturbations of diagonalizable normal operators acting boundedly on separable, infinite-dimensional complex Hilbert spaces, we will show that a large class of such operators are decomposable, extending in particular recent results of Foias, Jung, Ko and Pearcy.
Decomposable operators were introduced by Foias in the sixties and many operators in Hilbert spaces are decomposable as unitary operators, self-adjoint operators or more generally normal operators. In a broad sense, decomposable operators have the most general kind of spectral decomposition possible. Consequently, every operator in the aforementioned class has a rich spectral structure and plenty of non-trivial closed hyperinvariant subspaces.
Based on joint works with F. J. González-Doña.