The Invariant Subspace Problem: general operator theory vs. concrete operator theory

05.02.2016, 11 - 12.30  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Isabelle Chalendar (Lyon)

The Invariant Subspace Problem for (separable) Hilbert spaces is
a long-standing open question that traces back to John Von Neumann's works
in the 1950s asking, in particular, if every bounded linear operator
acting on an infinite dimensional separable Hilbert space has a
non-trivial closed invariant subspace. Whereas there are well-known
classes of bounded linear operators on Hilbert spaces that are known to
have non-trivial, closed invariant subspaces (normal operators, compact
operators, and polynomial compact operators), the question of
characterizing the lattice of the invariant subspaces of just a particular
bounded linear operator is known to be extremely difficult and indeed, it
may solve the Invariant Subspace Problem. In this expository talk, we will
focus on those concrete operators that may solve the invariant subspace
problem.