Invariant suspaces and upper triangular forms for classes of infinite dimensional operators


Tuesday, 5 November, 2013 - 12:00


Room 4082, Red Centre Building, UNSW


School of Mathematics and Statistics

Type of event: 


Presenter:  Ken Dykema

Institution: Texas A&M University


In classical matrix theory, a matrix can be written in upper triangular form with help of its invariant subspaces. A similar result, due to Ringrose in 1962, holds for compact operators on infinite dimensional Hilbert space.

Using recent results of Haagerup and Schultz, we prove an analogous result for certain non-compact operators on Hilbert space, namely, for those in finite von Neumann algebras.

The talk may also include some speculation about invariant subspace problems for elements of finite von Neumann algebras.  (Joint work with Fedor Sukochev and Dmitriy Zanin).