Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
梁玉霞,天津师范大学
Inviter:
Title:
Quasi-nilpotent operators and non-Euclidean metrics on resolvent set
Time & Venue:
2019.7.1 16:00-17:00 N602
Abstract:
A quasi-nilpotent operator on a Hilbert space has spectrum . ?Douglas and Rongwei Yang defined and studied the Hermitian metric on the resolvent set induced by the complex (1,1)-form , where is fixed with . In this report, I will introduce the non-Euclidean Hermitian metric on . Secondly, the formulas for the length of circles?and the energy functionals over circles are presented under this non-Euclidean Hermitian metric and their extremal equations are obtained. ?Especially, the energy functional of Volterra operator on is investigated in details, which can indicate some relations with invariant subspaces problem.