Fixed Points in Topological *-Algebras of Unbounded Operators

TL;DR

This paper investigates fixed point equations in topological *-algebras of unbounded operators, establishing existence results for weak τ strict contractions and exploring their continuity, with potential applications in quantum mechanics.

Contribution

It introduces the concept of weak τ strict contractions and provides existence and continuity results within topological *-algebras, extending fixed point theory to unbounded operators.

Findings

Existence of fixed points for weak τ strict contractions.

Continuity properties of these contraction maps.

Potential applications to quantum mechanical systems.

Abstract

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 {\em weak $\tau$ strict contractions}, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems.