Characterisations of open multivalued linear operators
Volume 175 / 2006
Studia Mathematica 175 (2006), 205-212
MSC: Primary 47A06.
DOI: 10.4064/sm175-3-1
Abstract
The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.
