Weakly concave operators

We investigate a class of left-invertible operators,
which we refer to as weakly concave operators. The motivation for this
study comes primarily from the wandering subspace problem for
norm-increasing m-isometries, m > 2. The class of weakly concave operators
includes all concave operators as well as a non-trivial class of
norm-increasing strict m-isometries with m > 2. We obtain a Wold-type
decomposition for weakly concave operators. As an application, we derive a
Berger-Shaw-type theorem for analytic weakly concave operators.

This talk is based on a joint work with Jan Stochel.