Academic
07 Mar 2019
- Title: Wandering subspace problem for norm-increasing m-isometries
- Abstract: The wandering subspace problem for an analytic norm-increasing m-isometry T on a Hilbert space H asks whether every T-invariant subspace of H can be generated by a wandering subspace. We captilize on the idea of weighted shift on the one-circuit directed graph to construct a family of analytic cyclic 3-isometries, which do not admit the wandering subspace property and which are norm-increasing on the orthogonal complement of a one-dimensional space. Further, on this one dimensional space, their norms can be made arbitrarily close to 1. This answers a question posed by Shimorin [Pg 185, Crelle, 2001] to a large extent (the case in which expansivity fails at one point). This is joint work with Shailesh Trivedi.
- Date & Day: 7th March’19/Thursday
- Time : 12:15 PM to 1:15 PM
- Venue: B117
