Speaker：Liu liu (Dalian University of Technology)

Time：2025-8-28 11:00

Location：Conference Room S105 at Experiment Building at Haiyun Campus

Abstract:

We introduce the concept of Davis-Wielandt Shell for an unbounded linear operator, which is a generalization of the numerical range. Give the relationships between the spectrum and the Davis-Wielandt Shell. The spectral inclusions for the sum and product of two linear operators are derived by utilizing the Davis-Wielandt Shells. Moreover, we list some resolvent estimates based on the DW shell, overcoming the limitation that resolvent estimates induced by the numerical range may be invalid for certain points in the resolvent set. We show that the upper bounds for norms of resolvents maybe tighter than those obtained from the numerical range, together with some sharp inequalities that improve some existing inequalities involving the numerical radius. Also, we geive descriptions of the DW-shell for some composition operators on the Hardy space.