Metric and homogeneous structure of closed range operators

G. CORACH; A. MAESTRIPIERI; M. MBEKHTA

JOURNAL OF OPERATOR THEORY

THETA FOUNDATION

Año: 2009 vol. 61 p. 171 - 190

0379-4024

Let C R be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topo- logical properties of C R if certain natural metrics are considered on it. We also define an action of the group GH × GK on C R and determine the orbits of this action. These orbits, which are strongly related to the connected compo- nents for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of C R.