Hilbert spaces and narrative economics: A formal operator-theoretic framework for story-driven macroeconomic dynamics

Narratives shape beliefs, influence expectations, propagate through populations, and affect macroeconomic dynamics. Behavioral economics has documented systematic deviations from rationality, while narrative economics emphasizes that stories spread epidemically and move asset prices, consumption, investment, and policy. This paper develops a rigorous mathematical framework integrating these insights using Hilbert-space methods and operator theory. Beliefs and narratives are represented as vectors in a complete inner-product space; propagation, distortion, and contagion are modeled by linear and nonlinear operators; and macroeconomic expectations emerge as projections of narrative vectors onto relevant economic directions. We derive conditions for viral amplification, exponential forgetting, the existence and uniqueness of stationary narrative states, and the stability of narrative-driven inflation and output expectations. Behavioral distortions such as availability, anchoring, and herding are formalized as nonlinear perturbations. The framework provides a unified structure for incorporating narratives into modern macroeconomic theory without abandoning mathematical rigor.