Fixed Points in Topological *-Algebras of Unbounded Operators

We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called weak τ strict contractions, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems. Running title: Fixed Points in Topological *-Algebras. Dipartimento di Matematica ed Applicazioni, Fac. Ingegneria, Università di Palermo, I-90128 Palermo, Italy. e-mail: [email protected] 2000 Mathematics Subject Classifications: 46N50, 47H10 Communicated by T. Kawai, July 14, 2000. Revised January 16, 2001