# The invariant subspace problem for bounded linear relations on Hlbert spaces

*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