Quaternionic Cayley transforms revisited
by
Florian-Horia Vasilescu
Department of Mathematics, University of Lille 1, France

It is well known that the classical Cayley transform can be extended to not necessarily bounded symmetric operators in Hilbert spaces, by a construction due to von Neumann. The operator Cayley transform does not seem to have useful properties when applied to operators which are no longer symmetric. For this reason, in order to find a similar formula for (formally) normal operators, one is leaded to consider a quaternionic framework. An attempt to extend this transform using the context of quaternions has been already made in the past by the author of this text. Recently, the previous definition has been replaced by an equivalent one, whose simplified form allows us to get the properties of the quaternionic Cayley transform from the usual Cayley transform for symmetric operators.

Date received: June 13, 2008