School Seminars and Colloquia

The invariant subspace problem for bounded linear relations on Hlbert spaces

Geometry/Topology Seminar

by Daniel Grixti-Cheng


Institution: The University of Melbourne
Date: Fri 2nd November 2007
Time: 11:00 AM
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: Linear relations (also known as Multivalued linear operators) were first
mentioned in a functional analytic context by John von Neumann. As linear relations are being observed with increasing occurrence in many areas of analysis, differential equations, continuum mechanics, control theory and mathematical economics, the theory of linear relations is steadily gaining popularity through applications to these fields of study. The importance
of linear relations has, more importantly, come to be recognised as the theory provides a more unified, general, and transparent treatment of modern operator theory than can be achieved through single valued
operators.

We consider the invariant subspace problem for linear relations on Hilbert spaces with the aim of promoting interest in the problem as viewed from the theory of linear relations. We present an equivalence between the single valued and multivalued invariant subspace problems and give some new theorems pertaining to the invariant subspace problem for linear relations
on a Hilbert space.

For More Information: Daniel Grixti-Cheng D.Grixti@ms.unimelb.edu.au